# How do you simplify [(xy^6)/(x^3y)]^-2?

Mar 25, 2018

$\implies {x}^{4} / {y}^{10}$

#### Explanation:

$\implies {\left[\frac{x {y}^{6}}{{x}^{3} y}\right]}^{-} 2$

We multiply all powers by $- 2$:

$\implies \frac{{x}^{- 2} {y}^{6 \left(- 2\right)}}{{x}^{3 \left(- 2\right)} {y}^{- 2}}$

Simplifying powers:

$\implies \frac{{x}^{-} 2 {y}^{-} 12}{{x}^{-} 6 {y}^{-} 2}$

Division of terms with powers requires subtraction of powers:

$\implies {x}^{- 2 - \left(- 6\right)} {y}^{- 12 - \left(- 2\right)}$

Simplifying:

$\implies {x}^{4} {y}^{-} 10$

We can get rid of negative powers by moving $y$ to the denominator:

$\implies {x}^{4} / {y}^{10}$