1. $2x^4y^{-2}\cdot 2^4x^4y^{12}$
$2^5x^8y^{10}\Rightarrow 32x^8y^{10}$
2. $2a^{-2}b^{-3}\cdot 2^4b^{16}$
$32a^{-2}b^{13}\Rightarrow \dfrac{32b^{13}}{a^2}$
3. $2^4x^8y^8\cdot x^{-4}$
$2^4x^4y^8\Rightarrow 16x^4y^8$
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5. $2x^{-3--3}y^{2-3}3^{-2}$
$2\cancel{x^0}y^{-1}3^{-2}\Rightarrow \dfrac{2}{9y}$
6. $3y^3\div [6x^7y^{-2}]$
$3x^{-7}y^{3--2}\div 6$
$3x^{-7}y^5\div 6 \Rightarrow \dfrac{y^5}{2x^7}$
7. $2y\div y^8$
$2y^{1-8}$
$2y^{-7}\Rightarrow \dfrac{2}{y^7}$
8. $a^{16}\div 2b\Rightarrow \dfrac{a^{16}}{2b}$
9. $2^4a^8b^{12}\div a^{-1}$
$16a^{8+1}b^{12}$
$16a^9b^{12}$
10. ${2}^{-2}{y}^{8}\div {x}^{2}\Rightarrow \dfrac{{y}^{8}}{{2}^{2}{x}^{2}}\Rightarrow \dfrac{{y}^{8}}{{4x}^{2}}$
11. $2^4m^4n^{4--2}$
$16m^4n^6$
12. $2x^{-3}\div x^{-4}y^3$
$2x^{-3--4}y^{-3}\Rightarrow 2xy^{-3} \Rightarrow \dfrac{2x}{y^3}$
13. $[2u^{-2}v^3\cdot 2^{-1}u^{-1}v^{-4}]\div 2u^{-4}$
$[u^{-3}v^{-1}]\div 2u^{-4}$
$2^{-1}u^{-3--4}v^{-1}$
$2^{-1}uv^{-1}\Rightarrow \dfrac{u}{2v}$
14. $2y \div 2^{-1}y^{-4}$
$2y\cdot 2y^4 \Rightarrow 4y^5$
15. $b^{-1}\div 2a^{-3}b^2$
$b^{-1}\cdot 2^{-1}a^3b^{-2}\Rightarrow \dfrac{a^3}{2b^3}$
16. $2x^2yz \div [2x^4y^4z^{-2}z^4y^8]$
$2x^2yz \div [2x^4y^{12}z^2]$
$2x^2yz \cdot z^{-1}x^{-4}y^{-12}z^{-2}$
$x^{-2}y^{-11}z^{-1}\Rightarrow \dfrac{1}{x^2y^{11}z}$
17. $2a^{-3}b^2c^2b^6\div a^9b^{-6}c^9$
$2a^{-3}b^8c^2\cdot a^{-9}b^6c^{-9}$
$2a^{-12}b^{14}c^{-7}\Rightarrow \dfrac{2b^{14}}{a^{12}c^7}$
18. $2m^2p^2q^5 \div [2^3m^3\cdot 4^3p^6]$
$2m^2p^2q^5 \div [2^3m^3\cdot 2^6p^6]$
$2m^2p^2q^5 \div 2^9m^3p^6$
$2m^2p^2q^5\cdot 2^{-9}m^{-3}p^{-6}$
$2^{-8}m^{-1}p^{-4}q^5\Rightarrow \dfrac{q^5}{2^8mp^4}\Rightarrow \dfrac{q^5}{256mp^4}$
19. $y^{-1}x^4z^{-2}\div x^2y^3z^2$
$y^{-1}x^4z^{-2}\cdot x^{-2}y^{-3}z^{-2}$
$x^2y^{-4}z^{-4}\Rightarrow \dfrac{x^2}{y^4z^4}$
20. $2mpn^{-3}\div 2n^2n^{-12}p^6$
$2mpn^{-3}\div 2n^{-10}p^6$
$2mpn^{-3}\cdot 2^{-1}n^{10}p^{-6}$
$mp^{-5}n^7\Rightarrow \dfrac{mn^7}{p^5}$