{"id":90,"date":"2021-06-02T01:50:44","date_gmt":"2021-06-02T01:50:44","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/1-2\/"},"modified":"2026-03-13T20:25:00","modified_gmt":"2026-03-13T20:25:00","slug":"1-2","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/1-2\/","title":{"raw":"1.1 Algebraic Expressions","rendered":"1.1 Algebraic Expressions"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, it is expected that you will be able to:\r\n<ul>\r\n \t<li>Use variables and algebraic symbols<\/li>\r\n \t<li>Identify expressions and equations<\/li>\r\n \t<li>Simplify expressions with exponents<\/li>\r\n \t<li>Simplify expressions using the order of operations<\/li>\r\n \t<li>Evaluate algebraic expressions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Use Variables and Algebraic Symbols<\/h1>\r\nIn algebra, letters of the alphabet are used to represent variables.\r\nLetters often used for variables are \\(x,y,a,b,\\text{and}\\phantom{\\rule{0.2em}{0ex}}c\\).\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Variables and Constants<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">A variable is a letter that represents a number or quantity whose value may change.<\/div>\r\n<div class=\"textbox__content\">A constant is a number whose value always stays the same.<\/div>\r\n<\/div>\r\nTo write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. There are four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.\r\n<table style=\"width: 100%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"left\">Operation<\/th>\r\n<th scope=\"col\" data-align=\"left\">Notation<\/th>\r\n<th scope=\"col\" data-align=\"left\">Say:<\/th>\r\n<th scope=\"col\" data-align=\"left\">The result is\u2026<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Addition<\/td>\r\n<td data-align=\"left\">\\(a+b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{plus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\r\n<td data-align=\"left\">the sum of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Subtraction<\/td>\r\n<td data-align=\"left\">\\(a-b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{minus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\r\n<td data-align=\"left\">the difference of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Multiplication<\/td>\r\n<td data-align=\"left\">\\(a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)\\)<\/td>\r\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\r\n<td data-align=\"left\">The product of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Division<\/td>\r\n<td data-align=\"left\">\\(a\\div b,a\/b,\\phantom{\\rule{0.2em}{0ex}}\\frac{a}{b},b\\overline{)a}\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) divided by \\(b\\)<\/td>\r\n<td data-align=\"left\">The quotient of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn algebra, the cross symbol, \u00d7, is not used to show multiplication because that symbol may cause confusion. Does \\(3xy\\) mean \\(3 \\phantom{\\rule{0.2em}{0ex}} \\times \\phantom{\\rule{0.2em}{0ex}}y\\) (three times \\(y\\)) or \\(3 \\cdot x \\cdot y\\) (three times \\(x\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}y\\))? To make it clear, use \u2022 or parentheses for multiplication.When two quantities have the same value, we say they are equal and connect them with an <em>equal sign<\/em>.\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Equality Symbol<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\\(a=b\\) is read \u201c\\(a\\) is equal to \\(b\\)\u201d<\/div>\r\n<div class=\"textbox__content\">The symbol \\(=\\) is called the <span class=\"no-emphasis\" data-type=\"term\">equal sign<\/span>.<\/div>\r\n<\/div>\r\nAn <span class=\"no-emphasis\" data-type=\"term\">inequality<\/span> is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that \\(b\\) is greater than \\(a\\), it means that \\(b\\) is to the right of \\(a\\) on the number line. We use the symbols &lt; and &gt; for inequalities.\r\n<div id=\"fs-id2650456\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Inequality<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id3202723\">\\(a\\) &lt; \\(b\\) is read \\(a\\) is less than \\(b\\)<\/p>\r\n<p id=\"fs-id2700412\">\\(a\\) is to the left of \\(b\\) on the number line<\/p>\r\n<span id=\"fs-id1933083\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_001-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id2495460\">\\(a\\) &gt; \\(b\\) is read \\(a\\) is greater than \\(b\\)<\/p>\r\n<p id=\"fs-id1379804\">\\(a\\) is to the right of \\(b\\) on the number line<\/p>\r\n<span id=\"fs-id1467098\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_002-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<p class=\"p1\">The expressions \\(a\\) &lt; \\(b\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}a\\) &gt; \\(\\phantom{\\rule{0.2em}{0ex}}b\\) can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,<\/p>\r\n<img class=\"alignnone wp-image-13451 size-full\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/Screenshot-2021-02-22-at-8.59.13-AM.png\" alt=\"&quot;7 is less than 11&quot; equivalent to &quot;11 is greater than 7&quot;\" width=\"2394\" height=\"222\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id2903489\">When we write an inequality symbol with a line under it, such as \\(a\\le b\\), it means \\(a&lt;b\\) or \\(a=b\\). We read this \\(a\\) is less than or equal to \\(b\\). Also, if we put a slash through an equal sign, \\(\\ne\\) it means \"not equal.\"<\/p>\r\n<p id=\"fs-id1238987\">We summarize the symbols of equality and inequality in the table below.<\/p>\r\n\r\n<table class=\"grid\" style=\"width: 100%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Algebraic Notation<\/th>\r\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Say<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a=b\\)<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\ne b\\)<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is not equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) &lt; \\(b\\)<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is less than \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) &gt; \\(b\\)<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is greater than \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\le b\\)<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is less than or equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\ge b\\)<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\">\\(a\\) is greater than or equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Symbols &lt; and &gt;<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1508974\">The symbols &lt; and &gt; each have a smaller side and a larger side.<\/p>\r\n<p id=\"eip-id1168265897874\">smaller side &lt; larger side\r\nlarger side &gt; smaller side<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nThe smaller side of the symbol faces the smaller number and the larger faces the larger number.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1171104414920\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1573881\" data-type=\"exercise\">\r\n<div id=\"fs-id1614444\" data-type=\"problem\">\r\n\r\nGrouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. The table below lists three of the most commonly used grouping symbols in algebra.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<table id=\"fs-id2856176\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has four rows and two columns. The first row spans both columns and is a header reading \u201cCommon Grouping Symbols\u201d. The second row is labeled \u201cparentheses\u201d in the first column and the shows the open parentheses symbol followed by the close parentheses symbol. The third row is labeled \u201cBrackets\u201d in the first column and the shows the open square bracket symbol followed by the close square bracket symbol. The third row is labeled \u201cbraces\u201d in the first column and the shows the open curly brace symbol followed by the close curly brace symbol.\"><caption>Common Grouping Symbols<\/caption>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Name<\/th>\r\n<th scope=\"col\">Symbol<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">parentheses<\/td>\r\n<td style=\"text-align: left;\" data-align=\"center\">\\(\\left(\\phantom{\\rule{0.5em}{0ex}}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">brackets<\/td>\r\n<td style=\"text-align: left;\" data-align=\"center\">\\(\\left[\\phantom{\\rule{0.5em}{0ex}}\\right]\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">braces<\/td>\r\n<td style=\"text-align: left;\" data-align=\"center\">\\(\\left\\{\\phantom{\\rule{0.5em}{0ex}}\\right\\}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nHere are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.\r\n<div id=\"fs-id2221712\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(8\\left(14-8\\right)\\phantom{\\rule{4em}{0ex}}21-3\\left[2+4\\left(9-8\\right)\\right]\\phantom{\\rule{4em}{0ex}}24\\div \\left\\{13-2\\left[1\\left(6-5\\right)+4\\right]\\right\\}\\)<\/div>\r\n<h1>Identify Expressions and Equations<\/h1>\r\n<p id=\"fs-id2139102\">What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. \u201cRunning very fast\u201d is a phrase, but \u201cThe football player was running very fast\u201d is a sentence. A sentence has a subject and a verb.<\/p>\r\n<p id=\"fs-id1171104014483\">In algebra, we have <em data-effect=\"italics\">expressions<\/em> and <em data-effect=\"italics\">equations<\/em>. An <span class=\"no-emphasis\" data-type=\"term\">expression<\/span> is like a phrase. Here are some examples of expressions and how they relate to word phrases:<\/p>\r\n\r\n<table id=\"fs-id2472125\" style=\"width: 100%;\" summary=\"This table has five rows and three columns. The first row is a header row and it labels each column. The first column is labeled \u201cExpression\u201d, the second \u201cWords\u201d and the third \u201cPhrase\u201d. In the second row, under the \u201cExpression\u201d column is three plus five. Under the \u201cWords\u201d column is the phrase \u201cthree plus five\u201d. Under the \u201cPhrase\u201d column is the phrase \u201cthe sum of three and five\u201d. In the third row, under the \u201cExpression\u201d column is n minus one. Under the \u201cWords\u201d column is the phrase \u201cn minus one.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe difference of n and one.\u201d In the fourth row, under the \u201cExpression\u201d column is six times seven. Under the \u201cWords\u201d column is the phrase \u201csix times seven.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe product of six and seven.\u201d In the fifth row, under the \u201cExpression\u201d column is x divided by y. Under the \u201cWords\u201d column is the phrase \u201cx divided by y.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe quotient of x and y.\u201d\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"left\">Expression<\/th>\r\n<th scope=\"col\" data-align=\"left\">Words<\/th>\r\n<th scope=\"col\" data-align=\"left\">Phrase<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(3+5\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(3\\phantom{\\rule{0.2em}{0ex}}\\text{plus}\\phantom{\\rule{0.2em}{0ex}}5\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">the sum of three and five<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(n-1\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(n\\) minus one<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">the difference of \\(n\\) and one<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(6\\cdot 7\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(6\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}7\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">the product of six and seven<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(\\frac{x}{y}\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(x\\) divided by \\(y\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">the quotient of \\(x\\) and \\(y\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that the phrases do not form a complete sentence because the phrase does not have a verb. An <span class=\"no-emphasis\" data-type=\"term\">equation<\/span> is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:\r\n<table id=\"fs-id2658369\" style=\"width: 100%;\" summary=\"This table has six rows and two columns. The first row is a header row labeling each column. The first column is labeled \u201cEquation\u201d and the second \u201cSentence\u201d. In the second row, under the \u201cEquation\u201d column is three plus five equals eight. Under the \u201cSentence\u201d column is the sentence \u201cThe sum of three and five is equal to eight\u201d. In the third row, under the \u201cEquation\u201d column is n minus one equals fourteen. Under the \u201cSentence\u201d column is the Sentence \u201cThe difference of n and one equals fourteen.\u201d In the fourth row, under the \u201cEquation\u201d column is six times seven equals forty-two. Under the \u201cSentence\u201d column is the sentence \u201cThe product of six and seven is equal to forty-two.\u201d In the fifth row, under the \u201cEquation\u201d column is x equals fifty-three. Under the \u201cSentence\u201d column is the sentence \u201cx is equal to fifty-three.\u201d In the sixth row, under the \u201cEquation\u201d column is y plus nine equals two times y minus 3. Under the \u201cSentence\u201d column is the sentence \u201cy plus nine is equal to two y minus three.\u201d\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"left\">Equation<\/th>\r\n<th scope=\"col\" data-align=\"left\">Sentence<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(3+5=8\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">The sum of three and five is equal to eight.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(n-1=14\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(n\\) minus one equals fourteen.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(6\\cdot 7=42\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">The product of six and seven is equal to forty-two.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(x=53\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(x\\) is equal to fifty-three.<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(y+9=2y-3\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(y\\) plus nine is equal to two \\(y\\) minus three.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1365219\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Expressions and Equations<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAn expression is a number, a variable, or a combination of numbers and variables and operation symbols.\r\n<p id=\"fs-id2451266\">An equation is made up of two expressions connected by an equal sign.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1544580\">Determine if each is an expression or an equation:<\/p>\r\n\r\n<ol id=\"eip-id1168469631637\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}16-6=10\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}4\\cdot 2+1\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x\\div 25\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}y+8=40\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1584678\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1166346957031\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a. \\(\\phantom{\\rule{0.2em}{0ex}}16-6=10\\)<\/td>\r\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b. \\(\\phantom{\\rule{0.2em}{0ex}}4\\cdot 2+1\\)<\/td>\r\n<td>This is an expression\u2014no equal sign.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c. \\(\\phantom{\\rule{0.2em}{0ex}}x\\div 25\\)<\/td>\r\n<td>This is an expression\u2014no equal sign.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d. \\(\\phantom{\\rule{0.2em}{0ex}}y+8=40\\)<\/td>\r\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2650086\" data-type=\"problem\">\r\n<p id=\"fs-id1619065\">Determine if each is an expression or an equation:<\/p>\r\n\r\n<ol id=\"eip-id1168468600384\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}23+6=29\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}7\\cdot 3-7\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1346095\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<ol id=\"eip-id1168468285584\" class=\"circled\" type=\"a\">\r\n \t<li>equation<\/li>\r\n \t<li>expression<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Simplify Expressions with Exponents<\/h1>\r\n<p id=\"fs-id1392631\">To simplify a numerical expression means to do all the math possible. For example, to simplify \\(4\\cdot2+1\\) we\u2019d first multiply \\(4\\cdot2\\) to get \\(8\\) and then add the \\(1\\) to get \\(9\\). A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:<\/p>\r\n\r\n<div id=\"fs-id1308315\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(4\\cdot2+1\\)<\/div>\r\n<div id=\"fs-id2495596\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(8+1\\)<\/div>\r\n<div id=\"fs-id3016728\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(9\\)<\/div>\r\n<p id=\"fs-id2144760\">Suppose we have the expression \\(2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\). We could write this more compactly using exponential notation. Exponential notation is also called <strong>power<\/strong> and is used in algebra to represent a quantity multiplied by itself several times. We write \\(2\\cdot2\\cdot2\\) as \\({2}^{3}\\) and \\(2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\) as \\({2}^{9}\\). In expressions such as \\({2}^{3}\\), the \\(2\\) is called the base and the \\(3\\) is called the exponent. The exponent tells us how many factors of the base we have to multiply.<\/p>\r\n<span id=\"fs-id2149605\" data-type=\"media\" data-alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_003_img-1.jpg\" alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div id=\"fs-id2669230\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\text{means multiply three factors of 2}\\)<\/div>\r\n<p id=\"fs-id2295676\">We say \\({2}^{3}\\) is in exponential notation\u00a0 and \\(2\\cdot2\\cdot2\\) is in expanded notation.<\/p>\r\n\r\n<div id=\"fs-id1243267\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exponential Notation (Power)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id2283832\">For any expression \\({a}^{n},a\\) is a factor multiplied by itself \\(n\\) times if \\(n\\) is a positive integer.<\/p>\r\n\r\n<div id=\"fs-id1882026\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({a}^{n}\\text{means multiply}\\phantom{\\rule{0.2em}{0ex}}n\\phantom{\\rule{0.2em}{0ex}}\\text{factors of}\\phantom{\\rule{0.2em}{0ex}}a\\)<\/div>\r\n<span id=\"fs-id2284773\" data-type=\"media\" data-alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_010_img-1.jpg\" alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id2786021\">The expression \\({a}^{n}\\) is read \\(a\\) to the \\({n}^{th}\\) power.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nFor powers of \\(n=2\\) and \\(n=3\\), we have special names.\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1547556\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{l}{a}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{is read as}\\phantom{\\rule{0.2em}{0ex}}\\text{\"}a\\phantom{\\rule{0.2em}{0ex}}\\text{squared\"}\\\\ {a}^{3}\\phantom{\\rule{0.2em}{0ex}}\\text{is read as}\\phantom{\\rule{0.2em}{0ex}}\\text{\"}a\\phantom{\\rule{0.2em}{0ex}}\\text{cubed\"}\\end{array}\\)<\/div>\r\n<p id=\"fs-id1387277\">The table below lists some examples of expressions written in exponential notation.<\/p>\r\n\r\n<table id=\"fs-id1830286\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cExponential Notation\u201d and the second \u201cIn Words\u201d. The second row shows the number seven followed by the superscript two in the first column and the phrase \u201cseven to the second power, or seven squared\u201d in the second column. The next row shows the number five followed by the superscript three in the first column and the phrase \u201cfive to the third power, or five cubed\u201d in the second column. The next row shows the number nine followed by the superscript four in the first column and the phrase \u201cnine to the fourth power\u201d in the second column. The last row shows the number twelve followed by the superscript five in the first column and the phrase \u201ctwelve to the fifth power\u201d in the second column.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"left\">Exponential Notation<\/th>\r\n<th scope=\"col\" data-align=\"center\">In Words<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\({7}^{2}\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(7\\) to the second power, or \\(7\\) squared<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\({5}^{3}\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(5\\) to the third power, or \\(5\\) cubed<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\({9}^{4}\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(9\\) to the fourth power<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"text-align: left;\" data-align=\"left\">\\({12}^{5}\\)<\/td>\r\n<td style=\"text-align: left;\" data-align=\"left\">\\(12\\) to the fifth power<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div data-type=\"example\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2692026\" data-type=\"problem\">\r\n<p id=\"fs-id1969755\">Write each expression in exponential form:<\/p>\r\n\r\n<ol id=\"eip-id1168469525719\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}16\\cdot16\\cdot16\\cdot16\\cdot16\\cdot16\\cdot16\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}9\\cdot9\\cdot9\\cdot9\\cdot9\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x\\cdot x\\cdot x\\cdot x\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}a\\cdot a\\cdot a\\cdot a\\cdot a\\cdot a\\cdot a\\cdot a\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id4124564\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1168469627334\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a. The base 16 is a factor 7 times.<\/td>\r\n<td>\\({16}^{7}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b. The base 9 is a factor 5 times.<\/td>\r\n<td>\\({9}^{5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c. The base \\(x\\) is a factor 4 times.<\/td>\r\n<td>\\({x}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d. The base \\(a\\) is a factor 8 times.<\/td>\r\n<td>\\({a}^{8}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2214154\" data-type=\"problem\">\r\n<p id=\"fs-id1859717\">Write each expression in exponential form:<\/p>\r\n<p id=\"fs-id1611515\">\\(41\\cdot41\\cdot41\\cdot41\\cdot41\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2276750\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<p id=\"fs-id1377278\">41<sup>5<\/sup><\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1171103024968\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id2669743\" data-type=\"exercise\">\r\n<div id=\"fs-id1345426\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1842666\" data-type=\"problem\">\r\n<p id=\"fs-id2270606\">Write each exponential expression in expanded form:<\/p>\r\n\r\n<ol id=\"eip-id1168469513220\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{8}^{6}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{x}^{5}\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id2150233\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id3177573\">a. The base is \\(8\\) and the exponent is \\(6\\), so \\({8}^{6}\\) means \\(8\\cdot 8\\cdot 8\\cdot 8\\cdot 8\\cdot 8\\)<\/p>\r\n<p id=\"fs-id2845374\">b. The base is \\(x\\) and the exponent is \\(5\\), so \\({x}^{5}\\) means \\(x\\cdot x\\cdot x\\cdot x\\cdot x\\)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2150329\" data-type=\"problem\">\r\n<p id=\"fs-id1337149\">Write each exponential expression in expanded form:<\/p>\r\n\r\n<ol id=\"eip-id1168466675879\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{4}^{8}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{a}^{7}\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1245764\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<ol id=\"eip-id1168466512417\" class=\"circled\" type=\"a\">\r\n \t<li>\\(4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4 \\cdot 4\\)<\/li>\r\n \t<li>\\(a \\cdot a \\cdot a \\cdot a \\cdot a \\cdot a \\cdot a\\)<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id2661619\">To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1603288\">Simplify: \\({3}^{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1762208\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1164752752096\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td data-align=\"center\">\\({3}^{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Expand the expression.<\/td>\r\n<td data-align=\"center\">\\(3\\cdot 3\\cdot 3\\cdot 3\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply left to right.<\/td>\r\n<td data-align=\"center\">\\(9\\cdot 3\\cdot 3\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td data-align=\"center\">\\(27\\cdot 3\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td data-align=\"center\">\\(81\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1578312\" data-type=\"problem\">\r\n<p id=\"fs-id2784369\">Simplify:<\/p>\r\n\r\n<ol id=\"eip-id1168466339424\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{5}^{3}\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}{1}^{7}\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id3294286\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<ol id=\"eip-id1168466339465\" class=\"circled\" type=\"a\">\r\n \t<li>125<\/li>\r\n \t<li>1<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Simplify Expressions Using the Order of Operations<\/h1>\r\n<p id=\"fs-id1357642\">We\u2019ve introduced most of the symbols and notation used in algebra, but now we need to clarify the <span class=\"no-emphasis\" data-type=\"term\">order of operations<\/span>. Otherwise, expressions may have different meanings, and they may result in different values.<\/p>\r\n<p id=\"fs-id1171101101203\">For example, consider the expression:<\/p>\r\n\r\n<div id=\"fs-id1171101101206\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(4+3\\cdot 7\\)<\/div>\r\n<div id=\"fs-id1171103305974\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill \\text{Some students say it simplifies to 49.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}&amp; &amp; \\hfill \\text{Some students say it simplifies to 25.}\\hfill \\\\ \\begin{array}{ccc}&amp; &amp; \\hfill 4+3\\cdot 7\\hfill \\\\ \\text{Since}\\phantom{\\rule{0.2em}{0ex}}4+3\\phantom{\\rule{0.2em}{0ex}}\\text{gives 7.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}&amp; \\hfill 7\\cdot 7\\hfill \\\\ \\text{And}\\phantom{\\rule{0.2em}{0ex}}7\\cdot 7\\phantom{\\rule{0.2em}{0ex}}\\text{is 49.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}&amp; \\hfill 49\\hfill \\end{array}&amp; &amp; &amp; \\begin{array}{ccc}&amp; &amp; \\hfill 4+3\\cdot 7\\hfill \\\\ \\phantom{\\rule{0.2em}{0ex}}\\text{Since}\\phantom{\\rule{0.2em}{0ex}}3\\cdot 7\\phantom{\\rule{0.2em}{0ex}}\\text{is 21.}\\hfill &amp; &amp; \\hfill 4+21\\hfill \\\\ \\phantom{\\rule{0.2em}{0ex}}\\text{And}\\phantom{\\rule{0.2em}{0ex}}21+4\\phantom{\\rule{0.2em}{0ex}}\\text{makes 25.}\\hfill &amp; &amp; \\hfill 25\\hfill \\end{array}\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1530117\">Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.<\/p>\r\n\r\n<div id=\"fs-id1715524\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Order of Operations<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id2750738\">When simplifying mathematical expressions perform the operations in the following order:<\/p>\r\n<p id=\"fs-id1834652\">1. <strong data-effect=\"bold\">P<\/strong>arentheses and other Grouping Symbols<\/p>\r\n\r\n<ul id=\"fs-id1171104029952\" data-bullet-style=\"bullet\">\r\n \t<li>Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\r\n<\/ul>\r\n<p id=\"fs-id1570796\">2. <strong data-effect=\"bold\">E<\/strong>xponents<\/p>\r\n\r\n<ul id=\"fs-id1171104407077\" data-bullet-style=\"bullet\">\r\n \t<li>Simplify all expressions with exponents.<\/li>\r\n<\/ul>\r\n<p id=\"fs-id1894922\">3. <strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/p>\r\n\r\n<ul id=\"fs-id1171103140103\" data-bullet-style=\"bullet\">\r\n \t<li>Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\r\n<\/ul>\r\n<p id=\"fs-id3402451\">4. <strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/p>\r\n\r\n<ul id=\"fs-id1171104002792\" data-bullet-style=\"bullet\">\r\n \t<li>Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\r\n<\/ul>\r\nStudents often ask, \u201cHow will I remember the order?\u201d Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase.\r\n<p id=\"fs-id1269648\" style=\"text-align: center;\"><strong data-effect=\"bold\">P<\/strong>lease <strong data-effect=\"bold\">E<\/strong>xcuse <strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear <strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally.<\/p>\r\n\r\n<table id=\"fs-id1786633\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row spans both columns and is a header reading \u201cOrder of Operations\u201d. In the second row the first column contains the word please with the p in bold and the second column contains the word parentheses with the p in bold. In the next row the first column contains the word excuse with the first e in bold and the second column contains the word exponents with the first e in bold. The next row contains the phrase \u201cmy dear\u201d in the first column with the m in my and the d in dear in bold and the second column contains the phrase \u201cmultiplication and division\u201d with the m in multiplication and the d in division in bold. The last row contains the phrase \u201cAunt Sally\u201d in the first column with the a in aunt and the s in Sally in bold and the second column contains the phrase \u201caddition and subtraction with the a in addition and the s in subtraction in bold.\" data-label=\"\">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>lease<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>arentheses<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xcuse<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xponents<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally<\/td>\r\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1785127\">It\u2019s good that \u2018<strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear\u2019 goes together, as this reminds us that <strong data-effect=\"bold\">m<\/strong>ultiplication and <strong data-effect=\"bold\">d<\/strong>ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.<\/p>\r\n<p id=\"fs-id1389767\">Similarly, \u2018<strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally\u2019 goes together and so reminds us that <strong data-effect=\"bold\">a<\/strong>ddition and <strong data-effect=\"bold\">s<\/strong>ubtraction also have equal priority and we do them in order from left to right.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"eip-313\" class=\"manipulative-math\" data-type=\"note\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2588260\" data-type=\"problem\">\r\n<p id=\"fs-id1270576\">Simplify the expressions:<\/p>\r\n\r\n<ol id=\"eip-id1168467381591\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}4+3\\cdot 7\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(4+3\\right)\\cdot 7\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1164750479370\" style=\"width: 100%;\" summary=\"The table shows the expression four plus three times seven. On the next line it states are there any parentheses in the expression? No. The line below that states are there any exponents in the expression? No. The next line states is there any multiplication or division in the expression? Yes. The next line states Multiply first and is followed by the expression of four plus three times seven. The expression is now four plus twenty-one. The last operation is addition. Add four and twenty-one to get twenty-five.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>a.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164750479401\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply first.<\/td>\r\n<td><span id=\"eip-id1164754094653\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><span id=\"eip-id1164754094670\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164754094685\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1164754514704\" class=\"unnumbered unstyled\" summary=\"The image shows the expression four plus three in parentheses times seven. Are there any parentheses? Yes, simplify inside the parentheses by adding four and three to get seven. The expression is now seven times seven. Is there any multiplication or division? Yes, multiply seven by seven to get forty-nine.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>b.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164754514734\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Are there any <strong>p<\/strong>arentheses? Yes.<\/td>\r\n<td><span id=\"eip-id1164754514754\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside the parentheses.<\/td>\r\n<td><span id=\"eip-id1164754514771\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1164754514814\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1496028\" data-type=\"problem\">\r\n<p id=\"fs-id2132962\">Simplify the expressions:<\/p>\r\n\r\n<ol id=\"eip-id1168467165875\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}12-5\\cdot 2\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\left(12-5\\right)\\cdot 2\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1732185\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<ol id=\"eip-id1168468411163\" class=\"circled\" type=\"a\">\r\n \t<li>2<\/li>\r\n \t<li>14<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2877215\" data-type=\"problem\">\r\n<p id=\"fs-id2308683\">Simplify: \\(18\\div 6+4\\left(5-2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id4127406\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1164754213917\" style=\"width: 100%;\" summary=\"The image shows the expression eighteen divided by six plus four, in parentheses, five minus two. Are there any parentheses? Yes, perform the subtraction inside the parentheses. Five minus two becomes three inside the parentheses. The expression is now eighteen divided by six plus four, in parentheses, three. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Divide first because multiplication and division are performed left to right. Divide eighteen by six to get three. The expression is now three plus four, in parentheses, three. Now multiply four by the three in parentheses to get twelve. The expression becomes three plus twelve. Add three and twelve to get fifteen.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164754213936\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Parentheses? Yes, subtract first.<\/td>\r\n<td><span id=\"eip-id1164752719997\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Exponents? No.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiplication or division? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide first because we multiply and divide left to right.<\/td>\r\n<td><span id=\"fs-id1166567548482\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Any other multiplication or division? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1164752720057\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Any other multiplication or division? No.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Any addition or subtraction? Yes.<\/td>\r\n<td><span id=\"eip-id1164752720083\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2876989\" data-type=\"problem\">\r\n<p id=\"fs-id2876984\">Simplify:<\/p>\r\n<p id=\"fs-id2876991\">\\(30\\div 5+10\\left(3-2\\right)\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2626124\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<p id=\"fs-id2626126\">16<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id2563008\">When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2563015\" data-type=\"problem\">\r\n<p id=\"fs-id2563017\">\\(\\text{Simplify:}\\phantom{\\rule{0.2em}{0ex}}5+{2}^{3}+3\\left[6-3\\left(4-2\\right)\\right]\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2308936\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1164754129434\" style=\"width: 100%;\" summary=\"The image shows the expression five plus two cubed plus three, open bracket, six minus three, open parentheses, four minus two close parentheses, close bracket. Are there any parentheses (or other grouping symbols)? Yes, there are parentheses within brackets. Start with the innermost grouping, the parentheses. Inside the parentheses subtract two from four to get two. The expression becomes five plus two cubed plus three, open bracket, six minus three, in parentheses, two, close bracket. Within the brackets is six minus three, in parentheses, two. Multiply three by two since multiplication comes before subtraction. The expression becomes five plus two cubed plus three, in brackets, six minus six. Finish simplifying inside the brackets by performing the subtraction. Six minus six leaves zero. The expression is now five plus two cubed plus three, in brackets, zero. Are there exponents? Yes, two cubed is eight and the expression becomes five plus eight plus three, in brackets, zero. Is there any multiplication or division? Yes, multiply three by zero to get zero. The expression is now five plus eight plus zero. The remaining operations are both addition. Perform the addition from left to right. five plus eight is thirteen. Thirteen plus zero is thirteen.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164754129452\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Are there any parentheses (or other grouping symbol)? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Focus on the parentheses that are inside the brackets.<\/td>\r\n<td><span id=\"eip-id1164754129478\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td><span id=\"eip-id1164754129495\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Continue inside the brackets and multiply.<\/td>\r\n<td><span id=\"eip-id1164754129512\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Continue inside the brackets and subtract.<\/td>\r\n<td><span id=\"eip-id1164754129529\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The expression inside the brackets requires no further simplification.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Are there any exponents? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify exponents.<\/td>\r\n<td><span id=\"eip-id1164752650667\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is there any multiplication or division? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1164752650693\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-07-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is there any addition or subtraction? Yes.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><span id=\"eip-id1164752650718\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-08-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><span id=\"eip-id1164752650735\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-09-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164752650751\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-10-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2308958\" data-type=\"problem\">\r\n<p id=\"fs-id2308953\">Simplify:<\/p>\r\n<p id=\"fs-id2308960\">\\(9+{5}^{3}-\\left[4\\left(9+3\\right)\\right]\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1956245\" data-type=\"solution\"><details><summary>Show Answer<\/summary>\r\n<p id=\"fs-id1956247\">86<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id2308949\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id2308956\" data-type=\"exercise\">\r\n<div id=\"fs-id1956245\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1956307\" data-type=\"problem\">\r\n<p id=\"fs-id1956309\">Simplify: \\({2}^{3}+{3}^{4}\\div 3-{5}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1956342\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-id1164754324162\" style=\"width: 100%;\" summary=\"The image shows the expression two cubed plus three to the fourth divided by three minus five squared. Are there any parentheses? No. Are there any exponents? Yes, several. Simplify each exponent. Two cubed is eight, three to the fourth is eighty-one, and five squared is twenty-five. The expression becomes eight plus eighty-one divided by three minus twenty-five. Is there any multiplication or division? Yes, just division. Divide eighty-one by three to get twenty-seven. The expression is now eight plus twenty-seven minus five. There is both addition and subtraction left. Perform these from left to right. Eight plus twenty-seven is thirty-five. Now the expression is thirty-five minus twenty five which leaves ten.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164754324181\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If an expression has several exponents, they may be simplified in the same step.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify exponents.<\/td>\r\n<td><span id=\"eip-id1164754324206\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td><span id=\"eip-id1164754324223\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><span id=\"eip-id1164754324240\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td><span id=\"eip-id1164754324256\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1164754324272\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1956364\" data-type=\"problem\">\r\n<p id=\"fs-id1956359\">Simplify:<\/p>\r\n\\({3}^{2}+{2}^{4}\\div 2+{4}^{3}\\)\r\n\r\n<\/div>\r\n<div id=\"fs-id1956396\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\r\n<p id=\"fs-id1956399\">81<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Evaluate Algebraic Expressions<\/h1>\r\n<p id=\"fs-id2907739\">In the last section, we simplified expressions using the order of operations. In this section, we\u2019ll evaluate expressions\u2014again following the order of operations.<\/p>\r\n<p id=\"fs-id1632121\">To evaluate an algebraic expression means to find the value of the expression when the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> is replaced by a given number. To evaluate an <span class=\"no-emphasis\" data-type=\"term\">expression<\/span>, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2603896\" data-type=\"problem\">\r\n<p id=\"fs-id1800944\">Evaluate \\(9x-2,\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\r\n\r\n<ol id=\"eip-id1168468470077\" class=\"circled\" type=\"a\">\r\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}x=5\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\r\n \t<li>\u00a0\\(\\phantom{\\rule{0.2em}{0ex}}x=1\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1406199\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id2311961\">Remember \\(ab\\) means \\(a\\) times \\(b\\), so \\(9x\\) means \\(9\\) times \\(x\\).<\/p>\r\n<p id=\"fs-id3177480\">a. To evaluate the expression when \\(x=5\\), we substitute \\(5\\) for \\(x\\), and then simplify.<\/p>\r\n\r\n<table id=\"eip-id1168469462966\" style=\"width: 100%;\" summary=\"The image shows the given expression nine x minus 2. Substitute 5 for x. The expression becomes 9 times 5 minus 2. Multiply first. Nine times 5 is 45 and the expression is now 45 minus 2. Subtract to get 43.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1168469462986\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1168469463000\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1168469463011\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1168469463028\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td><span id=\"eip-id1168469463045\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id2440233\">b. To evaluate the expression when \\(x=1\\), we substitute \\(1\\) for \\(x\\), and then simplify.<\/p>\r\n\r\n<table id=\"eip-id1168468440939\" style=\"width: 100%;\" summary=\"The image shows the given expression nine x minus 2. Substitute 1 for x. The expression becomes 9 times 1 minus 2. Multiply first. Nine times 1 is 9 and the expression is now 9 minus 2. Subtract to get 7.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1168468440960\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1168468440974\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1168468440984\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1168468441002\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td><span id=\"eip-id1168468441019\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id2216151\">Notice that in part a) that we wrote \\(9\\cdot 5\\) and in part b) we wrote \\(9\\left(1\\right)\\). Both the dot and the parentheses tell us to multiply.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1368058\" data-type=\"problem\">\r\n<p id=\"fs-id2451489\">Evaluate:<\/p>\r\n<p id=\"fs-id2136380\">\\(8x-3,\\text{when}\\phantom{\\rule{0.2em}{0ex}}\\)<\/p>\r\n\r\n<ol id=\"eip-id1168469756827\" class=\"circled\" type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x=2\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}x=1\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\r\n<ol id=\"eip-id1168467257646\" class=\"circled\" type=\"a\">\r\n \t<li>\u00a013<\/li>\r\n \t<li>\u00a05<\/li>\r\n<\/ol>\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id2761352\" class=\"try\" data-type=\"note\"><\/div>\r\n<div id=\"fs-id1171103512900\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1792161\" data-type=\"exercise\">\r\n<div id=\"fs-id2420879\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2756986\" data-type=\"problem\">\r\n<p id=\"fs-id1811335\">Evaluate \\({x}^{2}\\) when \\(x=10\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2661268\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id2214943\">We substitute \\(10\\) for \\(x\\), and then simplify the expression.<\/p>\r\n\r\n<table id=\"eip-id1168468538199\" style=\"width: 100%;\" summary=\"The image shows the given expression x squared. Substitute 10 for x. The expression becomes 10 squared. By the definition of exponents, 10 squared is 10 times 10. Multiply to get 100.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1168468538220\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1168468538234\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1168468538245\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of exponent.<\/td>\r\n<td><span id=\"eip-id1168468538262\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1168468538279\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id2197016\">When \\(x=10\\), the expression \\({x}^{2}\\) has a value of \\(100\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1881940\" data-type=\"problem\">\r\n<p id=\"fs-id1283634\">Evaluate:<\/p>\r\n<p id=\"fs-id1498924\">\\({x}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=8\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2296111\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\r\n<p id=\"fs-id1806491\">64<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1863809\" data-type=\"problem\">\r\n<p id=\"fs-id1325186\">\\(\\text{Evaluate}\\phantom{\\rule{0.2em}{0ex}}{2}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=5\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2784321\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1731877\">In this expression, the variable is an exponent.<\/p>\r\n\r\n<table id=\"eip-id1168469574741\" style=\"width: 100%;\" summary=\"The image shows the given expression 2 to the power of x. Substitute 5 for x. The expression becomes 2 to the fifth power. By the definition of exponents, 2 to the fifth power is 2 times 2 times 2 times 2 times 2, or 5 factors of 2. Multiply from left to right to get 32.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1168469574762\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1168469574776\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1168469574787\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of exponent.<\/td>\r\n<td><span id=\"eip-id1168469574804\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1168469574821\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1547737\">When \\(x=5\\), the expression \\({2}^{x}\\) has a value of \\(32\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1171105339525\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id902234\" data-type=\"exercise\">\r\n<div id=\"fs-id2201260\" data-type=\"solution\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1410068\" data-type=\"exercise\">\r\n<div id=\"fs-id2609710\" data-type=\"problem\">\r\n<p id=\"fs-id2630090\">Evaluate:<\/p>\r\n<p id=\"fs-id2130634\">\\({2}^{x}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2136192\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\r\n<p id=\"fs-id1824352\">64<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1410068\" data-type=\"exercise\">\r\n<div id=\"fs-id2609710\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1891867\" data-type=\"problem\">\r\n<p id=\"fs-id2276108\">\\(\\text{Evaluate}\\phantom{\\rule{0.2em}{0ex}}3x+4y-6\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=10\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}y=2\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2439822\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id2264342\">This expression contains two variables, so we must make two substitutions.<\/p>\r\n\r\n<table id=\"eip-id1168467158036\" style=\"width: 100%;\" summary=\"The image shows the given expression three x plus four y minus 6. Substitute 10 for x and 2 for y. The expression becomes 3 times 10 plus 4 times 2 minus 6. Perform multiplication from left to right. Three times 10 is 30 and 4 times 2 is 8. The expression becomes 30 plus 8 minus 6. Add and subtract from left to right. Thirty plus 8 is 38. Thirty-eight minus 6 is 32.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1168467237223\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1168467237237\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1168467237247\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1168467237264\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add and subtract left to right.<\/td>\r\n<td><span id=\"eip-id1168467237280\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1470900\">When \\(x=10\\) and \\(y=2\\), the expression \\(3x+4y-6\\) has a value of \\(32\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1549196\" data-type=\"problem\">\r\n<p id=\"fs-id2267372\">Evaluate:<\/p>\r\n<p id=\"fs-id1160292\">\\(2x+5y-4\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=11\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}y=3\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1630119\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>33\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1369028\" data-type=\"exercise\">\r\n<div id=\"fs-id1549196\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1785986\" data-type=\"problem\">\r\n<p id=\"fs-id2657506\">\\(\\text{Evaluate}\\phantom{\\rule{0.2em}{0ex}}2{x}^{2}+3x+8\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=4\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1383958\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id2310003\">We need to be careful when an expression has a variable with an exponent. In this expression, \\(2{x}^{2}\\) means \\(2\\cdot x\\cdot x\\) and is different from the expression \\({\\left(2x\\right)}^{2}\\), which means \\(2x\\cdot 2x\\).<\/p>\r\n\r\n<table id=\"eip-id1168466011069\" style=\"width: 100%;\" summary=\"The image shows the given expression two x squared plus three x plus 8. Substitute 4 for each x. The expression becomes 2 times 4 squared plus 3 times 4 plus 8. Simplify exponents first. Four squared is 16 so the expression becomes 2 times 16 plus 3 times 4 plus 8. Next perform multiplication from left to right. Two times 16 is 32 and 3 times 4 is 12. The expression becomes 32 plus 12 plus 8. Add from left to right. Thirty-two plus 12 is 44. Forty-four plus 8 is 52.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1168466011092\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1168466011106\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1168466011116\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify \\({4}^{2}\\).<\/td>\r\n<td><span id=\"eip-id1168466011141\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1168466011158\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><span id=\"eip-id1168466011175\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id2454530\" data-type=\"problem\">\r\n<p id=\"fs-id2646106\">Evaluate:<\/p>\r\n<p id=\"fs-id2265086\">\\(3{x}^{2}+4x+1\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=3\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id2835764\" data-type=\"solution\"><details open=\"open\"><summary>Show Answer<\/summary>\r\n<p id=\"fs-id1299685\">40<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nACCESS ADDITIONAL ONLINE RESOURCES\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id2327301\" class=\"media-2\" data-type=\"note\">\r\n<ul id=\"fs-id2327307\" data-display=\"block\">\r\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderoperate\">Order of Operations<\/a><\/li>\r\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderbasic\">Order of Operations \u2013 The Basics<\/a><\/li>\r\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24Evalexpress\">Ex: Evaluate an Expression Using the Order of Operations<\/a><\/li>\r\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24evalexpress3\">Example 3: Evaluate an Expression Using The Order of Operations<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<table id=\"eip-id1168265095050\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">Operation<\/strong><\/th>\r\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">Notation<\/strong><\/th>\r\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">Say:<\/strong><\/th>\r\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">The result is\u2026<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Addition<\/td>\r\n<td data-align=\"left\">\\(a+b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{plus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\r\n<td data-align=\"left\">the sum of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Multiplication<\/td>\r\n<td data-align=\"left\">\\(a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)\\)<\/td>\r\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{times}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\r\n<td data-align=\"left\">The product of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Subtraction<\/td>\r\n<td data-align=\"left\">\\(a-b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\phantom{\\rule{0.2em}{0ex}}\\text{minus}\\phantom{\\rule{0.2em}{0ex}}b\\)<\/td>\r\n<td data-align=\"left\">the difference of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Division<\/td>\r\n<td data-align=\"left\">\\(a\\div b,a\/b,\\phantom{\\rule{0.2em}{0ex}}\\frac{a}{b},b\\overline{)a}\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) divided by \\(b\\)<\/td>\r\n<td data-align=\"left\">The quotient of \\(a\\) and \\(b\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul id=\"eip-740\">\r\n \t<li><strong>Equality Symbol<\/strong>\r\n<ul id=\"eip-id1168262501679\">\r\n \t<li>\\(a=b\\) is read as \\(a\\) is equal to \\(b\\)<\/li>\r\n \t<li>The symbol \\(=\\) is called the equal sign.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Inequality<\/strong>\r\n<ul id=\"eip-id1168263909662\">\r\n \t<li>\\(a\\) &lt; \\(b\\) is read \\(a\\) is less than \\(b\\)<\/li>\r\n \t<li>\\(a\\) is to the left of \\(b\\) on the number line\r\n<span id=\"eip-id1168264918525\" data-type=\"media\" data-alt=\"..\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_018_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\r\n \t<li>\\(a\\) &gt; \\(b\\) is read \\(a\\) is greater than \\(b\\)<\/li>\r\n \t<li>\\(a\\) is to the right of \\(b\\) on the number line\r\n<span id=\"eip-id1168264785219\" data-type=\"media\" data-alt=\"..\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_019_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<table id=\"eip-455\" style=\"width: 100%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"center\">Algebraic Notation<\/th>\r\n<th scope=\"col\" data-align=\"center\">Say<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(a=b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) is equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(a\\ne b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) is not equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(a\\) &lt; \\(b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) is less than \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(a\\) &gt; \\(b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) is greater than \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(a\\le b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) is less than or equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">\\(a\\ge b\\)<\/td>\r\n<td data-align=\"left\">\\(a\\) is greater than or equal to \\(b\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul id=\"eip-910\">\r\n \t<li><strong>Exponential Notation<\/strong>\r\n<ul id=\"eip-id1168266330675\">\r\n \t<li>For any expression \\({a}^{n}\\) is a factor multiplied by itself \\(n\\) times, if \\(n\\) is a positive integer.<\/li>\r\n \t<li>\\({a}^{n}\\) means multiply \\(n\\) factors of \\(a\\)\r\n<span id=\"eip-id1168266330736\" data-type=\"media\" data-alt=\"..\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_020_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\r\n \t<li>The expression of \\({a}^{n}\\) is read \\(a\\) to the \\(n\\text{th}\\) power.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p id=\"eip-908\"><strong>Order of Operations<\/strong> When simplifying mathematical expressions perform the operations in the following order:<\/p>\r\n\r\n<ul id=\"eip-id1168264820124\" data-bullet-style=\"bullet\">\r\n \t<li>Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\r\n \t<li>Exponents: Simplify all expressions with exponents.<\/li>\r\n \t<li>Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\r\n \t<li>Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\r\n<\/ul>\r\n<h1>Glossary<\/h1>\r\n<div class=\"textbox shaded\">\r\n<dl id=\"fs-id2645686\">\r\n \t<dt>expressions<\/dt>\r\n \t<dd id=\"fs-id2645692\">An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id2645696\">\r\n \t<dt>equation<\/dt>\r\n \t<dd id=\"fs-id2645701\">An equation is made up of two expressions connected by an equal sign.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<h1>1.1 Exercise Set<\/h1>\r\n<p id=\"eip-578\">In the following exercises, determine if each is an expression or an equation.<\/p>\r\n\r\n<ol class=\"twocolumn\">\r\n \t<li>\\(9\\cdot 6=54\\)<\/li>\r\n \t<li>\\(5\\cdot 4+3\\)<\/li>\r\n \t<li>\\(x+7\\)<\/li>\r\n \t<li>\\(y-5=25\\)<\/li>\r\n<\/ol>\r\n<p id=\"eip-595\">In the following exercises, write in exponential form.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"5\">\r\n \t<li>\\(3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\cdot 3\\)<\/li>\r\n \t<li>\\(x\\cdot x\\cdot x\\cdot x\\cdot x\\)<\/li>\r\n<\/ol>\r\n<p id=\"fs-id4333539\">In the following exercises, write in expanded form.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"7\">\r\n \t<li>\\({5}^{3}\\)<\/li>\r\n \t<li>\\({2}^{8}\\)<\/li>\r\n<\/ol>\r\n<p id=\"eip-246\">In the following exercises, simplify.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"9\">\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}3+8\\cdot 5\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.4em}{0ex}}\\)<\/li>\r\n \t<li>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{(3+8)}\\cdot \\text{5}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\\({2}^{3}-12 \\div \\left(9-5\\right)\\)<\/li>\r\n \t<li>\\(3\\cdot 8+5\\cdot 2\\)<\/li>\r\n \t<li>\\(2+8\\left(6+1\\right)\\)<\/li>\r\n \t<li>\\(4\\cdot 12\/8\\)<\/li>\r\n \t<li>\\(6+10\/2+2\\)<\/li>\r\n \t<li>\\(\\left(6+10\\right)\\div \\left(2+2\\right)\\)<\/li>\r\n \t<li>\\(20\\div 4+6\\cdot5\\)<\/li>\r\n \t<li>\\(20\\div \\left(4+6\\right)\\cdot 5\\)<\/li>\r\n \t<li>\\({4}^{2}+{5}^{2}\\)<\/li>\r\n \t<li>\\({\\left(4+5\\right)}^{2}\\)<\/li>\r\n \t<li>\\(3\\left(1+9\\cdot 6\\right)-{4}^{2}\\)<\/li>\r\n \t<li>\\(2\\left[1+3\\left(10-2\\right)\\right]\\)<\/li>\r\n<\/ol>\r\n<p id=\"eip-663\">In the following exercises, evaluate the expression for the given value.<\/p>\r\n\r\n<ol class=\"twocolumn\" start=\"22\">\r\n \t<li>\\(7x+8\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=2\\)<\/li>\r\n \t<li>\\(5x-4\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=6\\)<\/li>\r\n \t<li>\\({x}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=12\\)<\/li>\r\n \t<li>\\({x}^{3}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=3\\)<\/li>\r\n \t<li>\\({x}^{2}+3x-7\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=4\\)<\/li>\r\n \t<li>\\(2x+4y-5\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=7,y=8\\)<\/li>\r\n \t<li>\\({\\left(x-y\\right)}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}x=10,y=7\\)<\/li>\r\n \t<li>\\({a}^{2}+{b}^{2}\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}a=3,b=8\\)<\/li>\r\n \t<li>\\(2l+2w\\phantom{\\rule{0.2em}{0ex}}\\text{when}\\phantom{\\rule{0.2em}{0ex}}l=15,w=12\\)<\/li>\r\n<\/ol>\r\n<h1>Answers:<\/h1>\r\n<ol class=\"threecolumn\">\r\n \t<li>equation<\/li>\r\n \t<li>expression<\/li>\r\n \t<li>expression<\/li>\r\n \t<li>equation<\/li>\r\n \t<li>3<sup>7<\/sup><\/li>\r\n \t<li><em data-effect=\"italics\">x<\/em><sup>5<\/sup><\/li>\r\n \t<li>5 \u00d7 5 \u00d7 5<\/li>\r\n \t<li>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>43<\/li>\r\n \t<li>55<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>5<\/li>\r\n \t<li>34<\/li>\r\n \t<li>58<\/li>\r\n \t<li>6<\/li>\r\n \t<li>13<\/li>\r\n \t<li>4<\/li>\r\n \t<li>35<\/li>\r\n \t<li>10<\/li>\r\n \t<li>41<\/li>\r\n \t<li>81<\/li>\r\n \t<li>149<\/li>\r\n \t<li>50<\/li>\r\n \t<li>22<\/li>\r\n \t<li>26<\/li>\r\n \t<li>144<\/li>\r\n \t<li>27<\/li>\r\n \t<li>21<\/li>\r\n \t<li>41<\/li>\r\n \t<li>9<\/li>\r\n \t<li>73<\/li>\r\n \t<li>54<\/li>\r\n<\/ol>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cUse the Language of Algebra\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, it is expected that you will be able to:<\/p>\n<ul>\n<li>Use variables and algebraic symbols<\/li>\n<li>Identify expressions and equations<\/li>\n<li>Simplify expressions with exponents<\/li>\n<li>Simplify expressions using the order of operations<\/li>\n<li>Evaluate algebraic expressions<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use Variables and Algebraic Symbols<\/h1>\n<p>In algebra, letters of the alphabet are used to represent variables.<br \/>\nLetters often used for variables are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d0677cc1ef8b048f8fab638c1b7c9f0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#44;&#121;&#44;&#97;&#44;&#98;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"108\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Variables and Constants<\/p>\n<\/header>\n<div class=\"textbox__content\">A variable is a letter that represents a number or quantity whose value may change.<\/div>\n<div class=\"textbox__content\">A constant is a number whose value always stays the same.<\/div>\n<\/div>\n<p>To write algebraically, we need some symbols as well as numbers and variables. There are several types of symbols we will be using. There are four basic arithmetic operations: addition, subtraction, multiplication, and division. We will summarize them here, along with words we use for the operations and the result.<\/p>\n<table style=\"width: 100%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\">Operation<\/th>\n<th scope=\"col\" data-align=\"left\">Notation<\/th>\n<th scope=\"col\" data-align=\"left\">Say:<\/th>\n<th scope=\"col\" data-align=\"left\">The result is\u2026<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-38830949a60ce6786a6fdf6309482002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-04ba1b81da8ae280d26d1991b56eec6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#108;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\">the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b644d18119c5701b308f883bd50656d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d626cdf4753df75818707f16d7b6dc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7c63a9888ac8ae036ae37309dee0451c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#98;&#44;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6e4e96a7e0e7b4b2dc622423b51fc66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1dc71412a2af9fb0a0b48f86c64005ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#100;&#105;&#118;&#32;&#98;&#44;&#97;&#47;&#98;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#44;&#98;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -6px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In algebra, the cross symbol, \u00d7, is not used to show multiplication because that symbol may cause confusion. Does <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c6ca1b49e7bbd5453cebf69bacc11790_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\" \/> mean <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b6506b30a670b89e6ab1a81aeb6a2d5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/> (three times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>) or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-eb218ff670db6e07da5d07f602fc22fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"54\" style=\"vertical-align: -4px;\" \/> (three times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-75f96701922fe212597a2a9731e93400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"68\" style=\"vertical-align: -4px;\" \/>)? To make it clear, use \u2022 or parentheses for multiplication.When two quantities have the same value, we say they are equal and connect them with an <em>equal sign<\/em>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Equality Symbol<\/p>\n<\/header>\n<div class=\"textbox__content\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> is read \u201c<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>\u201d<\/div>\n<div class=\"textbox__content\">The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> is called the <span class=\"no-emphasis\" data-type=\"term\">equal sign<\/span>.<\/div>\n<\/div>\n<p>An <span class=\"no-emphasis\" data-type=\"term\">inequality<\/span> is used in algebra to compare two quantities that may have different values. The number line can help you understand inequalities. Remember that on the number line the numbers get larger as they go from left to right. So if we know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, it means that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> on the number line. We use the symbols &lt; and &gt; for inequalities.<\/p>\n<div id=\"fs-id2650456\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Inequality<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id3202723\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id2700412\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<\/p>\n<p><span id=\"fs-id1933083\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_001-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter a on the left then the letter b to its right.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id2495460\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id1379804\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<\/p>\n<p><span id=\"fs-id1467098\" data-type=\"media\" data-alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_002-1.jpg\" alt=\"The figure shows a horizontal number line that begins with the letter b on the left then the letter a to its right.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<p class=\"p1\">The expressions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71809cd3555d6e746725d2e12cbbcd52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dfda230d82d07c923aeb595245f74958_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> can be read from left-to-right or right-to-left, though in English we usually read from left-to-right. In general,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-13451 size-full\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/Screenshot-2021-02-22-at-8.59.13-AM.png\" alt=\"&quot;7 is less than 11&quot; equivalent to &quot;11 is greater than 7&quot;\" width=\"2394\" height=\"222\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id2903489\">When we write an inequality symbol with a line under it, such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22bb7f496e0a4516393886afb53ffa7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/>, it means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9b57677a3c7d31d00aea3cdd09443b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#60;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/>. We read this <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>. Also, if we put a slash through an equal sign, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec2abdb669c9bb51bbc68474d39dd99f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#101;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"13\" style=\"vertical-align: -4px;\" \/> it means &#8220;not equal.&#8221;<\/p>\n<p id=\"fs-id1238987\">We summarize the symbols of equality and inequality in the table below.<\/p>\n<table class=\"grid\" style=\"width: 100%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Algebraic Notation<\/th>\n<th style=\"width: 50%;\" scope=\"col\" data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8740efbef2c653ea7d353859ecc91afd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is not equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22bb7f496e0a4516393886afb53ffa7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4925aae9d8237338b0824392ba2d182a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#103;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Symbols &lt; and &gt;<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1508974\">The symbols &lt; and &gt; each have a smaller side and a larger side.<\/p>\n<p id=\"eip-id1168265897874\">smaller side &lt; larger side<br \/>\nlarger side &gt; smaller side<\/p>\n<\/div>\n<\/div>\n<p>The smaller side of the symbol faces the smaller number and the larger faces the larger number.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104414920\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1573881\" data-type=\"exercise\">\n<div id=\"fs-id1614444\" data-type=\"problem\">\n<p>Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in written language. They indicate which expressions are to be kept together and separate from other expressions. The table below lists three of the most commonly used grouping symbols in algebra.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<table id=\"fs-id2856176\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has four rows and two columns. The first row spans both columns and is a header reading \u201cCommon Grouping Symbols\u201d. The second row is labeled \u201cparentheses\u201d in the first column and the shows the open parentheses symbol followed by the close parentheses symbol. The third row is labeled \u201cBrackets\u201d in the first column and the shows the open square bracket symbol followed by the close square bracket symbol. The third row is labeled \u201cbraces\u201d in the first column and the shows the open curly brace symbol followed by the close curly brace symbol.\">\n<caption>Common Grouping Symbols<\/caption>\n<tbody>\n<tr>\n<th scope=\"col\">Name<\/th>\n<th scope=\"col\">Symbol<\/th>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">parentheses<\/td>\n<td style=\"text-align: left;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6e6dea679189f864ebb36ac42159ea16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"21\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">brackets<\/td>\n<td style=\"text-align: left;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6366aa9031ead5bd088fb8b907907f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\">braces<\/td>\n<td style=\"text-align: left;\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d1a935744eae2523b7d685715069ba6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"25\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.<\/p>\n<div id=\"fs-id2221712\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7598f6833080f5808d041872936979d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#49;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#91;&#50;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#52;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#49;&#51;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#91;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"591\" style=\"vertical-align: -5px;\" \/><\/div>\n<h1>Identify Expressions and Equations<\/h1>\n<p id=\"fs-id2139102\">What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. \u201cRunning very fast\u201d is a phrase, but \u201cThe football player was running very fast\u201d is a sentence. A sentence has a subject and a verb.<\/p>\n<p id=\"fs-id1171104014483\">In algebra, we have <em data-effect=\"italics\">expressions<\/em> and <em data-effect=\"italics\">equations<\/em>. An <span class=\"no-emphasis\" data-type=\"term\">expression<\/span> is like a phrase. Here are some examples of expressions and how they relate to word phrases:<\/p>\n<table id=\"fs-id2472125\" style=\"width: 100%;\" summary=\"This table has five rows and three columns. The first row is a header row and it labels each column. The first column is labeled \u201cExpression\u201d, the second \u201cWords\u201d and the third \u201cPhrase\u201d. In the second row, under the \u201cExpression\u201d column is three plus five. Under the \u201cWords\u201d column is the phrase \u201cthree plus five\u201d. Under the \u201cPhrase\u201d column is the phrase \u201cthe sum of three and five\u201d. In the third row, under the \u201cExpression\u201d column is n minus one. Under the \u201cWords\u201d column is the phrase \u201cn minus one.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe difference of n and one.\u201d In the fourth row, under the \u201cExpression\u201d column is six times seven. Under the \u201cWords\u201d column is the phrase \u201csix times seven.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe product of six and seven.\u201d In the fifth row, under the \u201cExpression\u201d column is x divided by y. Under the \u201cWords\u201d column is the phrase \u201cx divided by y.\u201d Under the \u201cPhrase\u201d column is the phrase \u201cthe quotient of x and y.\u201d\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\">Expression<\/th>\n<th scope=\"col\" data-align=\"left\">Words<\/th>\n<th scope=\"col\" data-align=\"left\">Phrase<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cf4c2a80a2ff2ee7907cea5334d164d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-762867bb15efea281f5d64de25ffebdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#108;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the sum of three and five<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f30b71e7fcec69d119f30f67cf09c975_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> minus one<\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> and one<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c5cb7d583240ff955f68f8efcb5977a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-adb8738f2ddf7a3a9576b69d8d89e6c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the product of six and seven<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5156593683f791fcfc08d98d0045ea64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -9px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">the quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An <span class=\"no-emphasis\" data-type=\"term\">equation<\/span> is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. The equal sign gives the verb. Here are some examples of equations:<\/p>\n<table id=\"fs-id2658369\" style=\"width: 100%;\" summary=\"This table has six rows and two columns. The first row is a header row labeling each column. The first column is labeled \u201cEquation\u201d and the second \u201cSentence\u201d. In the second row, under the \u201cEquation\u201d column is three plus five equals eight. Under the \u201cSentence\u201d column is the sentence \u201cThe sum of three and five is equal to eight\u201d. In the third row, under the \u201cEquation\u201d column is n minus one equals fourteen. Under the \u201cSentence\u201d column is the Sentence \u201cThe difference of n and one equals fourteen.\u201d In the fourth row, under the \u201cEquation\u201d column is six times seven equals forty-two. Under the \u201cSentence\u201d column is the sentence \u201cThe product of six and seven is equal to forty-two.\u201d In the fifth row, under the \u201cEquation\u201d column is x equals fifty-three. Under the \u201cSentence\u201d column is the sentence \u201cx is equal to fifty-three.\u201d In the sixth row, under the \u201cEquation\u201d column is y plus nine equals two times y minus 3. Under the \u201cSentence\u201d column is the sentence \u201cy plus nine is equal to two y minus three.\u201d\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\">Equation<\/th>\n<th scope=\"col\" data-align=\"left\">Sentence<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f251b590557dcb19113fbdb2ed254a90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#53;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">The sum of three and five is equal to eight.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f05c27bbfe4c10679cf87e80eb4691e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;&#61;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"83\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> minus one equals fourteen.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d318b4958469c6ee37c85dbd39d45f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#61;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\">The product of six and seven is equal to forty-two.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4eeb41e4a9dbb3013f1ac9d84c50015b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is equal to fifty-three.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9f1807d0072c0bdf9e3edb59dc1e9cb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#57;&#61;&#50;&#121;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> plus nine is equal to two <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> minus three.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1365219\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Expressions and Equations<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/p>\n<p id=\"fs-id2451266\">An equation is made up of two expressions connected by an equal sign.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1544580\">Determine if each is an expression or an equation:<\/p>\n<ol id=\"eip-id1168469631637\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-50c2b0b49d1dc61ada00090a1abf73b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#45;&#54;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"88\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bb6a0cdd1ffdceb123f2c31b46cff1b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ce9a2882a3fcc95c02f071706cd7a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#100;&#105;&#118;&#32;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-abe813531d91d3fd774fbe5e6174deee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#56;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1584678\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1166346957031\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-50c2b0b49d1dc61ada00090a1abf73b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#45;&#54;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"88\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\n<\/tr>\n<tr>\n<td>b. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bb6a0cdd1ffdceb123f2c31b46cff1b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/td>\n<td>This is an expression\u2014no equal sign.<\/td>\n<\/tr>\n<tr>\n<td>c. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1ce9a2882a3fcc95c02f071706cd7a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#100;&#105;&#118;&#32;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/td>\n<td>This is an expression\u2014no equal sign.<\/td>\n<\/tr>\n<tr>\n<td>d. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-abe813531d91d3fd774fbe5e6174deee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#43;&#56;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>This is an equation\u2014two expressions are connected with an equal sign.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2650086\" data-type=\"problem\">\n<p id=\"fs-id1619065\">Determine if each is an expression or an equation:<\/p>\n<ol id=\"eip-id1168468600384\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a558290ed20394aca20efb1db37f2be9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#51;&#43;&#54;&#61;&#50;&#57;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec827f55d20f8525312cdb1c1a54dc3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1346095\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468285584\" class=\"circled\" type=\"a\">\n<li>equation<\/li>\n<li>expression<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions with Exponents<\/h1>\n<p id=\"fs-id1392631\">To simplify a numerical expression means to do all the math possible. For example, to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e5bcdefd1364fe53e1d9f55e26c39b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/> we\u2019d first multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4b63cc3704237b82061627522aa907fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> to get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and then add the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> to get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>. A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:<\/p>\n<div id=\"fs-id1308315\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e5bcdefd1364fe53e1d9f55e26c39b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#50;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id2495596\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da4cd73586f94b2e8aa3caaa55128212_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id3016728\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"fs-id2144760\">Suppose we have the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-708f52894b212c80d74774828823b151_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"181\" style=\"vertical-align: 0px;\" \/>. We could write this more compactly using exponential notation. Exponential notation is also called <strong>power<\/strong> and is used in algebra to represent a quantity multiplied by itself several times. We write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a6fa2186368e6575cca8d555edfdf6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-708f52894b212c80d74774828823b151_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"181\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5b90f99714c54357ddf7d3aea0e1d1fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>. In expressions such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>, the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> is called the base and the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> is called the exponent. The exponent tells us how many factors of the base we have to multiply.<\/p>\n<p><span id=\"fs-id2149605\" data-type=\"media\" data-alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_003_img-1.jpg\" alt=\"The image shows the number two with the number three, in superscript, to the right of the two. The number two is labeled as \u201cbase\u201d and the number three is labeled as \u201cexponent\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id2669230\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f6310f7ab8a428d88b06bce703ff5b1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#101;&#97;&#110;&#115;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#32;&#116;&#104;&#114;&#101;&#101;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#111;&#102;&#32;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"256\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"fs-id2295676\">We say <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> is in exponential notation\u00a0 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a6fa2186368e6575cca8d555edfdf6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/> is in expanded notation.<\/p>\n<div id=\"fs-id1243267\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exponential Notation (Power)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2283832\">For any expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e4bb51256ecc9ffb84be2f323eb6bf7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#44;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -4px;\" \/> is a factor multiplied by itself <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> times if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is a positive integer.<\/p>\n<div id=\"fs-id1882026\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5975a21738a00b5a3947d0fc69fc644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#101;&#97;&#110;&#115;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#115;&#32;&#111;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"240\" style=\"vertical-align: -3px;\" \/><\/div>\n<p><span id=\"fs-id2284773\" data-type=\"media\" data-alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_010_img-1.jpg\" alt=\"At the top of the image is the letter a with the letter n, in superscript, to the right of the a. The letter a is labeled as \u201cbase\u201d and the letter n is labeled as \u201cexponent\u201d. Below this is the letter a with the letter n, in superscript, to the right of the a set equal to n factors of a.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id2786021\">The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-02553ae49d720703c253c7bcbf008617_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#110;&#125;&#94;&#123;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\" \/> power.<\/p>\n<\/div>\n<\/div>\n<p>For powers of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8b4c6cd9d27ba344abe355a47d378bb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-85761a607075b960ff00638d721cfe9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, we have special names.<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1547556\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d24124a58990e4ace21c3431f8dac79c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#114;&#101;&#97;&#100;&#32;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#34;&#125;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#113;&#117;&#97;&#114;&#101;&#100;&#34;&#125;&#92;&#92;&#32;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#114;&#101;&#97;&#100;&#32;&#97;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#34;&#125;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#117;&#98;&#101;&#100;&#34;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"186\" style=\"vertical-align: -12px;\" \/><\/div>\n<p id=\"fs-id1387277\">The table below lists some examples of expressions written in exponential notation.<\/p>\n<table id=\"fs-id1830286\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cExponential Notation\u201d and the second \u201cIn Words\u201d. The second row shows the number seven followed by the superscript two in the first column and the phrase \u201cseven to the second power, or seven squared\u201d in the second column. The next row shows the number five followed by the superscript three in the first column and the phrase \u201cfive to the third power, or five cubed\u201d in the second column. The next row shows the number nine followed by the superscript four in the first column and the phrase \u201cnine to the fourth power\u201d in the second column. The last row shows the number twelve followed by the superscript five in the first column and the phrase \u201ctwelve to the fifth power\u201d in the second column.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\">Exponential Notation<\/th>\n<th scope=\"col\" data-align=\"center\">In Words<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d832ca5a71393670c83317b52a256157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the second power, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> squared<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22a6de91ce40f10ddb25e6ea195347ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> to the third power, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> cubed<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8075dfc642680f4c4a50ad4e0ba4b830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the fourth power<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2a89f6a2f2291b0852fd67c1b816441_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#50;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"text-align: left;\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> to the fifth power<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"example\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2692026\" data-type=\"problem\">\n<p id=\"fs-id1969755\">Write each expression in exponential form:<\/p>\n<ol id=\"eip-id1168469525719\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0033b10a6dd7d2b27b7ef7c36d7e29ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"200\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-60be981d520594c1e2873bc95f7ffdcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#92;&#99;&#100;&#111;&#116;&#57;&#92;&#99;&#100;&#111;&#116;&#57;&#92;&#99;&#100;&#111;&#116;&#57;&#92;&#99;&#100;&#111;&#116;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-be9e23551c8a64813bb22553097a687a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"78\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-755235106995d203b2927c20a8e47ffd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"164\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id4124564\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1168469627334\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a. The base 16 is a factor 7 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-97a1705bd17af21623aedf88d3bac62b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#54;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b. The base 9 is a factor 5 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e51308d1f57d7b304d32e225017a6f97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#57;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c. The base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is a factor 4 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-159899034a68d14dd24abc2121923568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>d. The base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is a factor 8 times.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-429724eba970bc2bdecc03d1e9142f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2214154\" data-type=\"problem\">\n<p id=\"fs-id1859717\">Write each expression in exponential form:<\/p>\n<p id=\"fs-id1611515\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7c10328136ee46620d4de81d7ff5364c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;&#92;&#99;&#100;&#111;&#116;&#52;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"139\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2276750\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1377278\">41<sup>5<\/sup><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171103024968\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2669743\" data-type=\"exercise\">\n<div id=\"fs-id1345426\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1842666\" data-type=\"problem\">\n<p id=\"fs-id2270606\">Write each exponential expression in expanded form:<\/p>\n<ol id=\"eip-id1168469513220\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-631f93fc40c0b634d6d162c6cb67a109_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#56;&#125;&#94;&#123;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8832c40f001cb86061449db5d5a297b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id2150233\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id3177573\">a. The base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and the exponent is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-387099948263518cacda9166ae83f7db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#56;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e14ec2337a4f0583515b91ada307afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id2845374\">b. The base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and the exponent is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-48541f82788d9b97a870606bd6257cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2adb5a63ea93ccbbb7c1ebd935c511d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"102\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2150329\" data-type=\"problem\">\n<p id=\"fs-id1337149\">Write each exponential expression in expanded form:<\/p>\n<ol id=\"eip-id1168466675879\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27c49982b6230f50688b7fc841426899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#52;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-067d5fcc21aa848b50db34270ff4737d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#97;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1245764\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466512417\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d563189c27adf553abd8a7535a563263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"161\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9cfdc1c5410ac923ab039ed098198433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"142\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id2661619\">To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1603288\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e51d6feba44ebe62d8639ff84d02323_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1762208\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164752752096\" style=\"width: 100%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e51d6feba44ebe62d8639ff84d02323_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Expand the expression.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8d2978629f9062b8c180d8a21001968f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply left to right.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3e62258d03d957521f030ebd19cf3735_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5a00c7742fac01808aa384b1961e5823_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2fddb0fc050fd5cd8cec81b9bb162aa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1578312\" data-type=\"problem\">\n<p id=\"fs-id2784369\">Simplify:<\/p>\n<ol id=\"eip-id1168466339424\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-52be7f73b3501ccbfc2e4f6cb3721784_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ac97f89dd380a5501d405daf59b7f589_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"15\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id3294286\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168466339465\" class=\"circled\" type=\"a\">\n<li>125<\/li>\n<li>1<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Order of Operations<\/h1>\n<p id=\"fs-id1357642\">We\u2019ve introduced most of the symbols and notation used in algebra, but now we need to clarify the <span class=\"no-emphasis\" data-type=\"term\">order of operations<\/span>. Otherwise, expressions may have different meanings, and they may result in different values.<\/p>\n<p id=\"fs-id1171101101203\">For example, consider the expression:<\/p>\n<div id=\"fs-id1171101101206\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3f76903033453bfd676449bc26cf98e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/div>\n<div id=\"fs-id1171103305974\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-905a3391614c3d47c5b299936895f3bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#109;&#101;&#32;&#115;&#116;&#117;&#100;&#101;&#110;&#116;&#115;&#32;&#115;&#97;&#121;&#32;&#105;&#116;&#32;&#115;&#105;&#109;&#112;&#108;&#105;&#102;&#105;&#101;&#115;&#32;&#116;&#111;&#32;&#52;&#57;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#109;&#101;&#32;&#115;&#116;&#117;&#100;&#101;&#110;&#116;&#115;&#32;&#115;&#97;&#121;&#32;&#105;&#116;&#32;&#115;&#105;&#109;&#112;&#108;&#105;&#102;&#105;&#101;&#115;&#32;&#116;&#111;&#32;&#50;&#53;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#110;&#99;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#43;&#51;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#103;&#105;&#118;&#101;&#115;&#32;&#55;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#55;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#52;&#57;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#57;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#110;&#99;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#50;&#49;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#43;&#50;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#49;&#43;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#107;&#101;&#115;&#32;&#50;&#53;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"659\" style=\"vertical-align: -35px;\" \/><\/div>\n<p id=\"fs-id1530117\">Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.<\/p>\n<div id=\"fs-id1715524\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Order of Operations<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2750738\">When simplifying mathematical expressions perform the operations in the following order:<\/p>\n<p id=\"fs-id1834652\">1. <strong data-effect=\"bold\">P<\/strong>arentheses and other Grouping Symbols<\/p>\n<ul id=\"fs-id1171104029952\" data-bullet-style=\"bullet\">\n<li>Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<\/ul>\n<p id=\"fs-id1570796\">2. <strong data-effect=\"bold\">E<\/strong>xponents<\/p>\n<ul id=\"fs-id1171104407077\" data-bullet-style=\"bullet\">\n<li>Simplify all expressions with exponents.<\/li>\n<\/ul>\n<p id=\"fs-id1894922\">3. <strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/p>\n<ul id=\"fs-id1171103140103\" data-bullet-style=\"bullet\">\n<li>Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<p id=\"fs-id3402451\">4. <strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/p>\n<ul id=\"fs-id1171104002792\" data-bullet-style=\"bullet\">\n<li>Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<p>Students often ask, \u201cHow will I remember the order?\u201d Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase.<\/p>\n<p id=\"fs-id1269648\" style=\"text-align: center;\"><strong data-effect=\"bold\">P<\/strong>lease <strong data-effect=\"bold\">E<\/strong>xcuse <strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear <strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally.<\/p>\n<table id=\"fs-id1786633\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has five rows and two columns. The first row spans both columns and is a header reading \u201cOrder of Operations\u201d. In the second row the first column contains the word please with the p in bold and the second column contains the word parentheses with the p in bold. In the next row the first column contains the word excuse with the first e in bold and the second column contains the word exponents with the first e in bold. The next row contains the phrase \u201cmy dear\u201d in the first column with the m in my and the d in dear in bold and the second column contains the phrase \u201cmultiplication and division\u201d with the m in multiplication and the d in division in bold. The last row contains the phrase \u201cAunt Sally\u201d in the first column with the a in aunt and the s in Sally in bold and the second column contains the phrase \u201caddition and subtraction with the a in addition and the s in subtraction in bold.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>lease<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">P<\/strong>arentheses<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xcuse<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">E<\/strong>xponents<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">M<\/strong>ultiplication and <strong data-effect=\"bold\">D<\/strong>ivision<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally<\/td>\n<td style=\"width: 50%;\" data-align=\"left\"><strong data-effect=\"bold\">A<\/strong>ddition and <strong data-effect=\"bold\">S<\/strong>ubtraction<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1785127\">It\u2019s good that \u2018<strong data-effect=\"bold\">M<\/strong>y <strong data-effect=\"bold\">D<\/strong>ear\u2019 goes together, as this reminds us that <strong data-effect=\"bold\">m<\/strong>ultiplication and <strong data-effect=\"bold\">d<\/strong>ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.<\/p>\n<p id=\"fs-id1389767\">Similarly, \u2018<strong data-effect=\"bold\">A<\/strong>unt <strong data-effect=\"bold\">S<\/strong>ally\u2019 goes together and so reminds us that <strong data-effect=\"bold\">a<\/strong>ddition and <strong data-effect=\"bold\">s<\/strong>ubtraction also have equal priority and we do them in order from left to right.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"eip-313\" class=\"manipulative-math\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2588260\" data-type=\"problem\">\n<p id=\"fs-id1270576\">Simplify the expressions:<\/p>\n<ol id=\"eip-id1168467381591\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-218a3ed8eae38e558ab408222ffecff5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ea15cc34a5bdcd99b5e1abb3e0ca576_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164750479370\" style=\"width: 100%;\" summary=\"The table shows the expression four plus three times seven. On the next line it states are there any parentheses in the expression? No. The line below that states are there any exponents in the expression? No. The next line states is there any multiplication or division in the expression? Yes. The next line states Multiply first and is followed by the expression of four plus three times seven. The expression is now four plus twenty-one. The last operation is addition. Add four and twenty-one to get twenty-five.\" data-label=\"\">\n<tbody>\n<tr>\n<td>a.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164750479401\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply first.<\/td>\n<td><span id=\"eip-id1164754094653\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164754094670\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754094685\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_011_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1164754514704\" class=\"unnumbered unstyled\" summary=\"The image shows the expression four plus three in parentheses times seven. Are there any parentheses? Yes, simplify inside the parentheses by adding four and three to get seven. The expression is now seven times seven. Is there any multiplication or division? Yes, multiply seven by seven to get forty-nine.\" data-label=\"\">\n<tbody>\n<tr>\n<td>b.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754514734\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>p<\/strong>arentheses? Yes.<\/td>\n<td><span id=\"eip-id1164754514754\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify inside the parentheses.<\/td>\n<td><span id=\"eip-id1164754514771\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any <strong>e<\/strong>xponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is there any <strong>m<\/strong>ultiplication or <strong>d<\/strong>ivision? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164754514814\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_012_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1496028\" data-type=\"problem\">\n<p id=\"fs-id2132962\">Simplify the expressions:<\/p>\n<ol id=\"eip-id1168467165875\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-038b41cfc44a53c72e6db00269cb21a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#45;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9def8d2f4eea68e91aaad4b4f0a7d6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1732185\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168468411163\" class=\"circled\" type=\"a\">\n<li>2<\/li>\n<li>14<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2877215\" data-type=\"problem\">\n<p id=\"fs-id2308683\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aed2528509154128b4468a54a02337b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#100;&#105;&#118;&#32;&#54;&#43;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id4127406\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754213917\" style=\"width: 100%;\" summary=\"The image shows the expression eighteen divided by six plus four, in parentheses, five minus two. Are there any parentheses? Yes, perform the subtraction inside the parentheses. Five minus two becomes three inside the parentheses. The expression is now eighteen divided by six plus four, in parentheses, three. Are there any exponents? No. Is there any multiplication or division? Yes, there is both multiplication and division. Divide first because multiplication and division are performed left to right. Divide eighteen by six to get three. The expression is now three plus four, in parentheses, three. Now multiply four by the three in parentheses to get twelve. The expression becomes three plus twelve. Add three and twelve to get fifteen.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754213936\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Parentheses? Yes, subtract first.<\/td>\n<td><span id=\"eip-id1164752719997\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Exponents? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Divide first because we multiply and divide left to right.<\/td>\n<td><span id=\"fs-id1166567548482\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Any other multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752720057\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Any other multiplication or division? No.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Any addition or subtraction? Yes.<\/td>\n<td><span id=\"eip-id1164752720083\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_015_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2876989\" data-type=\"problem\">\n<p id=\"fs-id2876984\">Simplify:<\/p>\n<p id=\"fs-id2876991\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5b2557a2acec25cbc5ca292a9ae3c8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#92;&#100;&#105;&#118;&#32;&#53;&#43;&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id2626124\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id2626126\">16<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id2563008\">When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2563015\" data-type=\"problem\">\n<p id=\"fs-id2563017\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0925a6ac1373608a585730b984c7311e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#58;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#53;&#43;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#91;&#54;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"257\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2308936\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754129434\" style=\"width: 100%;\" summary=\"The image shows the expression five plus two cubed plus three, open bracket, six minus three, open parentheses, four minus two close parentheses, close bracket. Are there any parentheses (or other grouping symbols)? Yes, there are parentheses within brackets. Start with the innermost grouping, the parentheses. Inside the parentheses subtract two from four to get two. The expression becomes five plus two cubed plus three, open bracket, six minus three, in parentheses, two, close bracket. Within the brackets is six minus three, in parentheses, two. Multiply three by two since multiplication comes before subtraction. The expression becomes five plus two cubed plus three, in brackets, six minus six. Finish simplifying inside the brackets by performing the subtraction. Six minus six leaves zero. The expression is now five plus two cubed plus three, in brackets, zero. Are there exponents? Yes, two cubed is eight and the expression becomes five plus eight plus three, in brackets, zero. Is there any multiplication or division? Yes, multiply three by zero to get zero. The expression is now five plus eight plus zero. The remaining operations are both addition. Perform the addition from left to right. five plus eight is thirteen. Thirteen plus zero is thirteen.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754129452\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Are there any parentheses (or other grouping symbol)? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Focus on the parentheses that are inside the brackets.<\/td>\n<td><span id=\"eip-id1164754129478\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1164754129495\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Continue inside the brackets and multiply.<\/td>\n<td><span id=\"eip-id1164754129512\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Continue inside the brackets and subtract.<\/td>\n<td><span id=\"eip-id1164754129529\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>The expression inside the brackets requires no further simplification.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Are there any exponents? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td><span id=\"eip-id1164752650667\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Is there any multiplication or division? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1164752650693\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-07-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Is there any addition or subtraction? Yes.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164752650718\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-08-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164752650735\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-09-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164752650751\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_016_img-10-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2308958\" data-type=\"problem\">\n<p id=\"fs-id2308953\">Simplify:<\/p>\n<p id=\"fs-id2308960\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0c738327e6a736035e5d49618465c2cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#43;&#123;&#53;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#91;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1956245\" data-type=\"solution\">\n<details>\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1956247\">86<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2308949\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2308956\" data-type=\"exercise\">\n<div id=\"fs-id1956245\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956307\" data-type=\"problem\">\n<p id=\"fs-id1956309\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-307f9f50feea41acbfdeb58a5bdf6429_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#51;&#125;&#94;&#123;&#52;&#125;&#92;&#100;&#105;&#118;&#32;&#51;&#45;&#123;&#53;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1956342\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-id1164754324162\" style=\"width: 100%;\" summary=\"The image shows the expression two cubed plus three to the fourth divided by three minus five squared. Are there any parentheses? No. Are there any exponents? Yes, several. Simplify each exponent. Two cubed is eight, three to the fourth is eighty-one, and five squared is twenty-five. The expression becomes eight plus eighty-one divided by three minus twenty-five. Is there any multiplication or division? Yes, just division. Divide eighty-one by three to get twenty-seven. The expression is now eight plus twenty-seven minus five. There is both addition and subtraction left. Perform these from left to right. Eight plus twenty-seven is thirty-five. Now the expression is thirty-five minus twenty five which leaves ten.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754324181\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>If an expression has several exponents, they may be simplified in the same step.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td><span id=\"eip-id1164754324206\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td><span id=\"eip-id1164754324223\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1164754324240\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1164754324256\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1164754324272\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_017_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1956364\" data-type=\"problem\">\n<p id=\"fs-id1956359\">Simplify:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-188136b69a995071d61c1c511245fc67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#92;&#100;&#105;&#118;&#32;&#50;&#43;&#123;&#52;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1956396\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1956399\">81<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Evaluate Algebraic Expressions<\/h1>\n<p id=\"fs-id2907739\">In the last section, we simplified expressions using the order of operations. In this section, we\u2019ll evaluate expressions\u2014again following the order of operations.<\/p>\n<p id=\"fs-id1632121\">To evaluate an algebraic expression means to find the value of the expression when the <span class=\"no-emphasis\" data-type=\"term\">variable<\/span> is replaced by a given number. To evaluate an <span class=\"no-emphasis\" data-type=\"term\">expression<\/span>, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2603896\" data-type=\"problem\">\n<p id=\"fs-id1800944\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ba13a4de500b8e85ecc2a946289ec74a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#45;&#50;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/p>\n<ol id=\"eip-id1168468470077\" class=\"circled\" type=\"a\">\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f12ee10180053cf88736a2efc9e4fac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3865a7fcb98e87dd2fd1e2f10e80a7f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1406199\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2311961\">Remember <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7202c73e2795274765d7f01eefc3e3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, so <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c4dc36d20a7690e84c99b1c91d651a08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> times <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id3177480\">a. To evaluate the expression when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/>, we substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, and then simplify.<\/p>\n<table id=\"eip-id1168469462966\" style=\"width: 100%;\" summary=\"The image shows the given expression nine x minus 2. Substitute 5 for x. The expression becomes 9 times 5 minus 2. Multiply first. Nine times 5 is 45 and the expression is now 45 minus 2. Subtract to get 43.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469462986\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469463000\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168469463011\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168469463028\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168469463045\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_016_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2440233\">b. To evaluate the expression when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/>, we substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, and then simplify.<\/p>\n<table id=\"eip-id1168468440939\" style=\"width: 100%;\" summary=\"The image shows the given expression nine x minus 2. Substitute 1 for x. The expression becomes 9 times 1 minus 2. Multiply first. Nine times 1 is 9 and the expression is now 9 minus 2. Subtract to get 7.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468440960\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468440974\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168468440984\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468441002\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1168468441019\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_017_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2216151\">Notice that in part a) that we wrote <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cdfa2fe38b12384b657598414c4c1ba5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/> and in part b) we wrote <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3c641a98a34adadd81cea378969c5d6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\" \/>. Both the dot and the parentheses tell us to multiply.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1368058\" data-type=\"problem\">\n<p id=\"fs-id2451489\">Evaluate:<\/p>\n<p id=\"fs-id2136380\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6eec575b7214298a672afcdad3fe21da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#45;&#51;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -4px;\" \/><\/p>\n<ol id=\"eip-id1168469756827\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-27e167450fc28128ed466c1b1c929fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3865a7fcb98e87dd2fd1e2f10e80a7f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<ol id=\"eip-id1168467257646\" class=\"circled\" type=\"a\">\n<li>\u00a013<\/li>\n<li>\u00a05<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2761352\" class=\"try\" data-type=\"note\"><\/div>\n<div id=\"fs-id1171103512900\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1792161\" data-type=\"exercise\">\n<div id=\"fs-id2420879\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2756986\" data-type=\"problem\">\n<p id=\"fs-id1811335\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2661268\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2214943\">We substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>, and then simplify the expression.<\/p>\n<table id=\"eip-id1168468538199\" style=\"width: 100%;\" summary=\"The image shows the given expression x squared. Substitute 10 for x. The expression becomes 10 squared. By the definition of exponents, 10 squared is 10 times 10. Multiply to get 100.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168468538220\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168468538234\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168468538245\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td><span id=\"eip-id1168468538262\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168468538279\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_018_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2197016\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2c4b0a8a79b7bd0e6e72a5fca0be9982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1881940\" data-type=\"problem\">\n<p id=\"fs-id1283634\">Evaluate:<\/p>\n<p id=\"fs-id1498924\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fed379ea7db3c74d46255f30ef2e9a19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2296111\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1806491\">64<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1863809\" data-type=\"problem\">\n<p id=\"fs-id1325186\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1855f5269f0c29a8b2cceebd55c0394f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"178\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2784321\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1731877\">In this expression, the variable is an exponent.<\/p>\n<table id=\"eip-id1168469574741\" style=\"width: 100%;\" summary=\"The image shows the given expression 2 to the power of x. Substitute 5 for x. The expression becomes 2 to the fifth power. By the definition of exponents, 2 to the fifth power is 2 times 2 times 2 times 2 times 2, or 5 factors of 2. Multiply from left to right to get 32.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168469574762\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168469574776\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168469574787\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Use the definition of exponent.<\/td>\n<td><span id=\"eip-id1168469574804\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168469574821\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_019_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1547737\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d138fb64cc6a9225d06fdb1af9ca3a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105339525\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id902234\" data-type=\"exercise\">\n<div id=\"fs-id2201260\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1410068\" data-type=\"exercise\">\n<div id=\"fs-id2609710\" data-type=\"problem\">\n<p id=\"fs-id2630090\">Evaluate:<\/p>\n<p id=\"fs-id2130634\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d06d34886c4542fc6d28d686dce68431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#120;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"108\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2136192\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1824352\">64<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2134194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1410068\" data-type=\"exercise\">\n<div id=\"fs-id2609710\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1891867\" data-type=\"problem\">\n<p id=\"fs-id2276108\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-df75478c368b4adfddab4bce6fcb4516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#120;&#43;&#52;&#121;&#45;&#54;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"336\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2439822\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2264342\">This expression contains two variables, so we must make two substitutions.<\/p>\n<table id=\"eip-id1168467158036\" style=\"width: 100%;\" summary=\"The image shows the given expression three x plus four y minus 6. Substitute 10 for x and 2 for y. The expression becomes 3 times 10 plus 4 times 2 minus 6. Perform multiplication from left to right. Three times 10 is 30 and 4 times 2 is 8. The expression becomes 30 plus 8 minus 6. Add and subtract from left to right. Thirty plus 8 is 38. Thirty-eight minus 6 is 32.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168467237223\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168467237237\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168467237247\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168467237264\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add and subtract left to right.<\/td>\n<td><span id=\"eip-id1168467237280\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_020_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1470900\">When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6adca822887415d6f9a00ba1a1d97657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/>, the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-82c159a12d32f031e64d98abbc2acb45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#52;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/> has a value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1549196\" data-type=\"problem\">\n<p id=\"fs-id2267372\">Evaluate:<\/p>\n<p id=\"fs-id1160292\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c2c4d72d1b30fe01ea1d5ab6738e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#45;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"266\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1630119\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p>33<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1369028\" data-type=\"exercise\">\n<div id=\"fs-id1549196\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1785986\" data-type=\"problem\">\n<p id=\"fs-id2657506\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f149d2f0dfbdbca05e322af1d141715d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#69;&#118;&#97;&#108;&#117;&#97;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"259\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1383958\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id2310003\">We need to be careful when an expression has a variable with an exponent. In this expression, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ae30abf586092f073ce5550de99fde9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-56b20de91e0dcbf61d8c07b3d538e03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\" \/> and is different from the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b69fdfc9b1be5f69f62258f17748005a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -5px;\" \/>, which means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d464895f10d0ac50f4ac34048556ad4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<table id=\"eip-id1168466011069\" style=\"width: 100%;\" summary=\"The image shows the given expression two x squared plus three x plus 8. Substitute 4 for each x. The expression becomes 2 times 4 squared plus 3 times 4 plus 8. Simplify exponents first. Four squared is 16 so the expression becomes 2 times 16 plus 3 times 4 plus 8. Next perform multiplication from left to right. Two times 16 is 32 and 3 times 4 is 12. The expression becomes 32 plus 12 plus 8. Add from left to right. Thirty-two plus 12 is 44. Forty-four plus 8 is 52.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1168466011092\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-02-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1168466011106\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-01-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1168466011116\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-03-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-59cc891325714152bb52ef9a606aa546_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td><span id=\"eip-id1168466011141\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-04-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1168466011158\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-05-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><span id=\"eip-id1168466011175\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_02_021_img-06-1.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2454530\" data-type=\"problem\">\n<p id=\"fs-id2646106\">Evaluate:<\/p>\n<p id=\"fs-id2265086\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6fe49d50b6b73a50e7a7090677e544be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#120;&#43;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"188\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id2835764\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show Answer<\/summary>\n<p id=\"fs-id1299685\">40<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>ACCESS ADDITIONAL ONLINE RESOURCES<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id2327301\" class=\"media-2\" data-type=\"note\">\n<ul id=\"fs-id2327307\" data-display=\"block\">\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderoperate\">Order of Operations<\/a><\/li>\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24orderbasic\">Order of Operations \u2013 The Basics<\/a><\/li>\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24Evalexpress\">Ex: Evaluate an Expression Using the Order of Operations<\/a><\/li>\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24evalexpress3\">Example 3: Evaluate an Expression Using The Order of Operations<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<table id=\"eip-id1168265095050\" class=\"grid\" style=\"width: 100%;\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \u201cOperation\u201d, the second \u201cNotation\u201d, the third \u201cSay\u201d and the last \u201cThe result is...\u201d. Under the \u201cOperation\u201d column are the words: addition, multiplication, subtraction and division. Under the \u201cNotation\u201d column are algebraic expressions. The first row shows the letter a, the plus symbol, and the letter b. The next row shows four algebraic expressions. The first is the letter a, dot multiplication symbol, and the letter b. The second expression is the letter a in parentheses and the letter b in parentheses. The third expression is the letter a in parentheses and the letter b. The fourth expression is the letter a and the letter b in parentheses. The next row shows the letter a, the minus symbol, and the letter b. The last row shows four algebraic expressions. The first is the letter a, division symbol, and the letter b. The second expression is the letter a, the backslash symbol and the letter b. The third expression is the letter a above the fraction bar and the letter b below the fraction bar. The fourth expression is the letter b outside the division bracket and the letter a inside the division bracket.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">Operation<\/strong><\/th>\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">Notation<\/strong><\/th>\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">Say:<\/strong><\/th>\n<th scope=\"col\" data-align=\"left\"><strong data-effect=\"bold\">The result is\u2026<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-38830949a60ce6786a6fdf6309482002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-04ba1b81da8ae280d26d1991b56eec6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#108;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\">the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7c63a9888ac8ae036ae37309dee0451c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#98;&#44;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6e4e96a7e0e7b4b2dc622423b51fc66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The product of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b644d18119c5701b308f883bd50656d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d626cdf4753df75818707f16d7b6dc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#110;&#117;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1dc71412a2af9fb0a0b48f86c64005ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#100;&#105;&#118;&#32;&#98;&#44;&#97;&#47;&#98;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#44;&#98;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -6px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> divided by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\">The quotient of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-740\">\n<li><strong>Equality Symbol<\/strong>\n<ul id=\"eip-id1168262501679\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> is read as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8690b7efd237bfe32a6e92e3b699b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"4\" width=\"13\" style=\"vertical-align: 2px;\" \/> is called the equal sign.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Inequality<\/strong>\n<ul id=\"eip-id1168263909662\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<br \/>\n<span id=\"eip-id1168264918525\" data-type=\"media\" data-alt=\"..\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_018_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> on the number line<br \/>\n<span id=\"eip-id1168264785219\" data-type=\"media\" data-alt=\"..\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_019_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<table id=\"eip-455\" style=\"width: 100%;\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \u201cAlgebraic Notation\u201d, the second \u201cSay\u201d. Under the \u201cAlgebraic Notation\u201d column are the algebraic expressions: a equals b; a is not equal to b; a is less than b; a is greater than b; a is less than or equal to b; a is greater than or equal to b. Under the \u201cSay\u201d column are the phrases: \u201ca is equal to b\u201d, \u201ca is not equal to b\u201d, \u201ca is less than b\u201d, \u201ca is greater than b\u201d, \u201ca is less than or equal to b\u201d, and \u201ca is greater than or equal to b\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"center\">Algebraic Notation<\/th>\n<th scope=\"col\" data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e69295ccf8d8ca292abcc97f861e345f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8740efbef2c653ea7d353859ecc91afd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is not equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &lt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> &gt; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22bb7f496e0a4516393886afb53ffa7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is less than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4925aae9d8237338b0824392ba2d182a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#103;&#101;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -3px;\" \/><\/td>\n<td data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> is greater than or equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-910\">\n<li><strong>Exponential Notation<\/strong>\n<ul id=\"eip-id1168266330675\">\n<li>For any expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> is a factor multiplied by itself <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> times, if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> is a positive integer.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> means multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><br \/>\n<span id=\"eip-id1168266330736\" data-type=\"media\" data-alt=\"..\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2018\/12\/CNX_BMath_Figure_02_01_020_img-1.jpg\" alt=\"..\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<li>The expression of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef78644f25c125ead81d3c69ef32dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> is read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11349328cd25470084f3e0e831b97cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: 0px;\" \/> power.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p id=\"eip-908\"><strong>Order of Operations<\/strong> When simplifying mathematical expressions perform the operations in the following order:<\/p>\n<ul id=\"eip-id1168264820124\" data-bullet-style=\"bullet\">\n<li>Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<li>Exponents: Simplify all expressions with exponents.<\/li>\n<li>Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<li>Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id2645686\">\n<dt>expressions<\/dt>\n<dd id=\"fs-id2645692\">An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/dd>\n<\/dl>\n<dl id=\"fs-id2645696\">\n<dt>equation<\/dt>\n<dd id=\"fs-id2645701\">An equation is made up of two expressions connected by an equal sign.<\/dd>\n<\/dl>\n<\/div>\n<h1>1.1 Exercise Set<\/h1>\n<p id=\"eip-578\">In the following exercises, determine if each is an expression or an equation.<\/p>\n<ol class=\"twocolumn\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a39d1b47a661ee2eb192fe0ab13fa9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#61;&#53;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-342de3ffda17fdd03f01c8e849111391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dc75694098649a22421bc1ec912c0b09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f2829365cb54d13a68be79ab7be40b72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#45;&#53;&#61;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<p id=\"eip-595\">In the following exercises, write in exponential form.<\/p>\n<ol class=\"twocolumn\" start=\"5\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2d3785d6d191a86edd0c6ec5a1914b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"139\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2adb5a63ea93ccbbb7c1ebd935c511d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#92;&#99;&#100;&#111;&#116;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"102\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<p id=\"fs-id4333539\">In the following exercises, write in expanded form.<\/p>\n<ol class=\"twocolumn\" start=\"7\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-22a6de91ce40f10ddb25e6ea195347ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#53;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-202cb81727487a115a9ecd3ead290a93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<p id=\"eip-246\">In the following exercises, simplify.<\/p>\n<ol class=\"twocolumn\" start=\"9\">\n<li>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-81a36dbe71f4a460c0529815d6d51ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#43;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3937db2bf9317f1e4ad06463de0ac410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#40;&#51;&#43;&#56;&#41;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3a0ba3b058f7091614276649859a7fe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#32;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"130\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6988096d0f42cb96bcecb6061adb6b05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#56;&#43;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d1ad557dac274b0cecd3d0f2409d2881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-49e6efc78d7d5105a0a12a8e2a7b0802_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#50;&#47;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3c0309e2eddc9d9daaa38348b30a1ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#49;&#48;&#47;&#50;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bec6a099237ebd5279a1b29f8a24c095_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d73e8be75a139e1f66b3303cba6dd553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#100;&#105;&#118;&#32;&#52;&#43;&#54;&#92;&#99;&#100;&#111;&#116;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"100\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-decc556ae96382595bd947a469a05e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c63b437879b41a5f9d2b03e2395729f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#53;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-714768b56fa6f5935338e9e13d4a2ec8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-50afced7de346e9f24e899c17c7754a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#43;&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#123;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-30e1bf8798a5926bd4107059d2e499ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#91;&#49;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ol>\n<p id=\"eip-663\">In the following exercises, evaluate the expression for the given value.<\/p>\n<ol class=\"twocolumn\" start=\"22\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e16637eb089fba02244dee7c25a4b3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#43;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7cba914abc63d432a5a2b6d37e123c24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"140\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8ad3dfdc33f13dd73f9511eaf357b403_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"116\" style=\"vertical-align: -1px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b5d79562a052b56357118eb086e7b0d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"108\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f78d3e2ddf361fb6ca5b07cfc9793320_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#55;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"179\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b2e44810b7759d8205ca8d9240e2e3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#52;&#121;&#45;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#55;&#44;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"229\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-62575be5f7ce742d4e28435b9a853a41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#49;&#48;&#44;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"210\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-62c617a2febf82190b08efd9afdc7a11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#61;&#51;&#44;&#98;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-775b98022dabb968ad02e2f38a710f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#108;&#43;&#50;&#119;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#108;&#61;&#49;&#53;&#44;&#119;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"214\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<h1>Answers:<\/h1>\n<ol class=\"threecolumn\">\n<li>equation<\/li>\n<li>expression<\/li>\n<li>expression<\/li>\n<li>equation<\/li>\n<li>3<sup>7<\/sup><\/li>\n<li><em data-effect=\"italics\">x<\/em><sup>5<\/sup><\/li>\n<li>5 \u00d7 5 \u00d7 5<\/li>\n<li>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/li>\n<li>\n<ol type=\"a\">\n<li>43<\/li>\n<li>55<\/li>\n<\/ol>\n<\/li>\n<li>5<\/li>\n<li>34<\/li>\n<li>58<\/li>\n<li>6<\/li>\n<li>13<\/li>\n<li>4<\/li>\n<li>35<\/li>\n<li>10<\/li>\n<li>41<\/li>\n<li>81<\/li>\n<li>149<\/li>\n<li>50<\/li>\n<li>22<\/li>\n<li>26<\/li>\n<li>144<\/li>\n<li>27<\/li>\n<li>21<\/li>\n<li>41<\/li>\n<li>9<\/li>\n<li>73<\/li>\n<li>54<\/li>\n<\/ol>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse the Language of Algebra\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":125,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-90","chapter","type-chapter","status-publish","hentry"],"part":21,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/90","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":6,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/90\/revisions"}],"predecessor-version":[{"id":2196,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/90\/revisions\/2196"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/21"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/90\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=90"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=90"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=90"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=90"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}