Question

Simplify the following exponential expression. Show your work step by step and list the Properties of Exponents used to solve this problem next to your work.

Answer 1

Solution:

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2}$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =\frac{3(1)(2x^3y^2)^4}{(4x^7y^4)^2}$               Since, $a^0=1$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =\frac{3(2)^4(x^3)^4(y^2)^4}{(4)^2(x^7)^2(y^4)^2}$               Since, $(ab)^m=a^mb^m$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =\frac{3(16)x^{12}y^{8}}{16x^{14}y^{8}}$               Since, $(a^m)^n=a^{mn}$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =\frac{3x^{12}y^{8}}{x^{14}y^{8}}$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =3x^{12-14}y^{8-8}$               Since, $\frac{a^m}{a^n} =a^{m-n}, a^0=1$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =3x^{-2}y^{0}$

$\frac{3x^0(2x^3y^2)^4}{(4x^7y^4)^2} =\frac{3}{x^2}$