Question

Simplify 4(2x^3y^4)^4/2(2x^2y^6)^3. Show your work. Please help ASAP!!

Answer 1

Answer:

The simplified expression to the given expression is $\frac{4x^6}{y^2}$

Therefore $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}$

Step-by-step explanation:

Given fractional expression is $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}$

To simplify the given expression as below :

$\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}$

$=\frac{2(2x^3y^4)^4}{(2x^2y^6)^3}$

$=\frac{2[(2)^4(x^3)^4(y^4)^4]}{(2)^3(x^2)^3(y^6)^3}$  ( using the property $(a^m)^n=a^{mn}$)

$=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}$

$=2[(2)^4(x^{12})(y^{16})](2)^{-3}(x^{-6})(y^{-18})$  (  ( using the property $a^m=\frac{1}{a^{-m}}$ )

$=2[2^{4-3}x^{12-6}y^{16-18}]$( using the property $a^m.a^n=a^{m+n}$ )

$=2[2^1x^6y^{-2}]$

$=\frac{4x^6}{y^2}$ ( using the property $a^m=\frac{1}{a^{-m}}$ )

Therefore the simplified expression is $\frac{4x^6}{y^2}$

Therefore $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}$