How do you simplify \frac { x ^ { - 8} ( x ^ { - 2} y ^ { 2} ) ^ { 2} } { ( 4x ^ { - 4} ) ^ { 2} y ^ { 2} }?

1 Answer
Apr 23, 2018

(x^-8(x^-2y^2)^2)/((4x^-4)^2y^2)=y^2/(16x^4)

Explanation:

(x^-8(x^-2y^2)^2)/((4x^-4)^2y^2)

Let's loose the parenthesis first. Remember that

(x^m)^n=x^(mn).

(x^-8(x^-2y^2)^2)/((4x^-4)^2y^2)= (x^-8x^-4y^4)/(16x^-8y^2)

Now cancel. Remember that

(x^m)/(x^n)=x^(m-n).

(x^-8x^-4y^4)/(16x^-8y^2)=(x^-4y^2)/16

Now express everything with positive exponents. Remember that

x^-m=1/x^m

(x^-4y^2)/16=y^2/(16x^4)