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

Apr 23, 2018

$\frac{{x}^{-} 8 {\left({x}^{-} 2 {y}^{2}\right)}^{2}}{{\left(4 {x}^{-} 4\right)}^{2} {y}^{2}} = {y}^{2} / \left(16 {x}^{4}\right)$

#### Explanation:

$\frac{{x}^{-} 8 {\left({x}^{-} 2 {y}^{2}\right)}^{2}}{{\left(4 {x}^{-} 4\right)}^{2} {y}^{2}}$

Let's loose the parenthesis first. Remember that

${\left({x}^{m}\right)}^{n} = {x}^{m n}$.

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

Now cancel. Remember that

$\frac{{x}^{m}}{{x}^{n}} = {x}^{m - n}$.

$\frac{{x}^{-} 8 {x}^{-} 4 {y}^{4}}{16 {x}^{-} 8 {y}^{2}} = \frac{{x}^{-} 4 {y}^{2}}{16}$

Now express everything with positive exponents. Remember that

${x}^{-} m = \frac{1}{x} ^ m$

$\frac{{x}^{-} 4 {y}^{2}}{16} = {y}^{2} / \left(16 {x}^{4}\right)$