Answer Key 9.8
- [latex](2^4x^4y^6)^{\frac{1}{8}}\Rightarrow 2^{\frac{1}{2}}x^{\frac{1}{2}}y^{\frac{3}{4}}[/latex]
- [latex](3^2x^2y^6)^{\frac{1}{4}}\Rightarrow 3^{\frac{1}{2}}x^{\frac{1}{2}}y^{\frac{3}{2}}[/latex]
- [latex](2^6x^4y^6z^8)^{\frac{1}{12}}\Rightarrow 2^{\frac{1}{2}}x^{\frac{1}{3}}y^{\frac{1}{2}}z^{\frac{2}{3}}[/latex]
- [latex]\left(\dfrac{5^2x^3}{2^4x^5}\right)^{\frac{1}{8}}\Rightarrow \left(\dfrac{5^2}{2^4x^2}\right)^{\frac{1}{8}}\Rightarrow \dfrac{5^{\frac{1}{4}}}{2^{\frac{1}{2}}x^{\frac{1}{4}}}[/latex]
- [latex]\left(\dfrac{2^4x}{3^2y^4}\right)^{\frac{1}{6}}\Rightarrow \dfrac{2^{\frac{2}{3}}x^{\frac{1}{6}}}{3^{\frac{1}{3}}y^{\frac{2}{3}}}[/latex]
- [latex](x^9y^{12}z^6)^{\frac{1}{15}}\Rightarrow x^{\frac{3}{5}}y^{\frac{4}{5}}z^{\frac{2}{5}}[/latex]
- [latex](x^6y^9)^{\frac{1}{12}}\Rightarrow x^{\frac{1}{2}}y^{\frac{3}{4}}[/latex]
- [latex](2^6x^8y^4)^{\frac{1}{10}}\Rightarrow 2^{\frac{3}{5}}x^{\frac{4}{5}}y^{\frac{2}{5}}[/latex]
- [latex](x^6y^4z^2)^{\frac{1}{8}}\Rightarrow x^{\frac{3}{4}}y^{\frac{1}{2}}z^{\frac{1}{4}}[/latex]
- [latex](5^2y^2)^{\frac{1}{4}}\Rightarrow 5^{\frac{1}{2}}y^{\frac{1}{2}}[/latex]
- [latex](2^3x^3y^6)^{\frac{1}{9}}\Rightarrow 2^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/latex]
- [latex](3^4x^8y^{12})^{\frac{1}{16}}\Rightarrow 3^{\frac{1}{4}}x^{\frac{1}{2}}y^{\frac{3}{4}}[/latex]
- [latex]5^{\frac{1}{3}}\cdot 5^{\frac{1}{2}}\Rightarrow 5^{\frac{3}{6}}\cdot 5^{\frac{2}{6}}\Rightarrow 5^{\frac{5}{6}}[/latex]
- [latex]7^{\frac{1}{3}}\cdot 7^{\frac{1}{4}}\Rightarrow 7^{\frac{4}{12}}\cdot 7^{\frac{3}{12}}\Rightarrow 7^{\frac{7}{12}}[/latex]
- [latex]x^{\frac{1}{2}}\cdot 7^{\frac{1}{3}}x^{\frac{1}{3}}\Rightarrow 7^{\frac{1}{3}}x^{\frac{5}{6}}[/latex]
- [latex]y^{\frac{1}{3}}\cdot 3^{\frac{1}{5}}y^{\frac{1}{5}}\Rightarrow 3^{\frac{1}{5}}y^{\frac{8}{15}}[/latex]
- [latex]x^{\frac{1}{2}}\cdot x^{\frac{2}{3}}\Rightarrow x^{\frac{7}{6}}[/latex]
- [latex]3^{\frac{1}{4}}x^{\frac{1}{4}}x^{\frac{4}{2}}\Rightarrow 3^{\frac{1}{4}}x^{\frac{9}{4}}[/latex]
- [latex]x^{\frac{2}{5}}y^{\frac{1}{5}}x^{\frac{2}{2}}\Rightarrow x^{\frac{7}{5}}y^{\frac{1}{5}}[/latex]
- [latex]a^{\frac{1}{2}}b^{\frac{1}{2}}2^{\frac{1}{5}}a^{\frac{2}{5}}b^{\frac{2}{5}}\Rightarrow 2^{\frac{1}{5}}a^{\frac{9}{10}}b^{\frac{9}{10}}[/latex]
- [latex]x^{\frac{1}{4}}y^{\frac{2}{4}}\cdot x^{\frac{2}{3}}y^{\frac{1}{3}}\Rightarrow x^{\frac{11}{12}}y^{\frac{5}{6}}[/latex]
- [latex]3^{\frac{1}{5}}a^{\frac{2}{5}}b^{\frac{3}{5}}3^{\frac{2}{4}}a^{\frac{2}{4}}b^{\frac{1}{4}}\Rightarrow 3^{\frac{7}{10}}a^{\frac{9}{10}}b^{\frac{17}{20}}[/latex]
- [latex]a^{\frac{2}{4}}b^{\frac{1}{4}}c^{\frac{2}{4}}a^{\frac{2}{5}}b^{\frac{3}{5}}c^{\frac{1}{5}}\Rightarrow a^{\frac{9}{10}}b^{\frac{17}{20}}c^{\frac{7}{10}}[/latex]
- [latex]x^{\frac{2}{6}}y^{\frac{1}{6}}z^{\frac{3}{6}}x^{\frac{2}{5}}y^{\frac{1}{5}}z^{\frac{2}{5}}\Rightarrow x^{\frac{11}{15}}y^{\frac{11}{30}}z^{\frac{9}{10}}[/latex]
