1. $4^{1+4+4}=4^9\text{ or }262,144$
2. $4^{1+4+2}=4^7\text{ or }16,384$
3. $2\cdot 4\cdot m^{4+2}n^{2+1}=8m^6n^3$
4. $x^{2+1}y^{4+2}=x^3y^6$
5. $3^{3\cdot 4}=3^{12}\text{ or }531,441$
6. $4^{3\cdot 4}=4^{12}\text{ or }16,772,216$
7. $2^2u^{3\cdot 2}v^{2\cdot 2}=4u^6v^4$
8. $x^3y^3$
9. $4^{5-3}=4^2\text{ or }16$
10. $3^{7-3}=3^4\text{ or }81$
11. $3^{1-1}n^{1-1}m^2=\cancel{3^0} \cancel{n^0} m^2$
12. $4^{-1}x^{2-1}y^{4-1}=4^{-1}xy^3$
13. $(2x^{2+3}y^{4+3})^2$
$(2x^5y^7)^2$
$2^2x^{5\cdot 2}y^{7\cdot 2}$
$4x^{10}y^{14}$
14. $[2u^{2+4}v^2]^3$
$[2u^6v^2]^3$
$2^3u^{6\cdot 3}v^{2\cdot 3} \Rightarrow 8u^{18}v^6$
15. $[2^3x^3\div x^3]^2$
$[2^3x^{3-3}]^2$
$2^{3\cdot 2}\cancel{x^0}$
$2^6 \text{ or }64$
16. $2a^{2+7}b^2\div b^2a^{4\cdot 2}$
$2a^9b^2\div b^2a^8$
$2a^{9-8}\cancel{b^{2-2}}$
$2a$
17. $[2y^{17}\div 2^4x^{2\cdot 4}y^{4\cdot 4}]^3$
$[2y^{17}\div 2^4x^8y^{16}]^3$
$[2^{1-4}y^{17-16}x^{-8}]^3$
$[2^{-3}yx^{-8}]^3$
$2^{-9}y^3x^{-24}$
18. $[xy^2\cdot y^8]\div 2y^4$
$xy^{10}\div 2y^4$
$2^{-1}xy^{10-4}$
$2^{-1}xy^6$
19. $4x^3y^8\div 2xy^7$
$2x^2y$
20. $2y^3x^2\div x^4y^4$
$2x^{-2}y^{-1}$
21. $[q^3r^2\cdot 4p^4q^4r^6]\div 2p^3$
$4p^4q^7r^8\div 2p^3$
$2pq^7r^8$
22. $4x^6y^{12}z^{10}\div x^4y^8z^8$
$4x^2y^4z^2$