# How do you divide (x^4y^-2) /(x^-3y^5)?

Mar 23, 2018

${\left(\frac{x}{y}\right)}^{7}$

#### Explanation:

Division of like-terms will powers is equivalent to writing the term with the difference of the powers.

$\implies \frac{{x}^{4} {y}^{- 2}}{{x}^{- 3} {y}^{5}}$

We have ${x}^{4}$ in the numerator and ${x}^{- 3}$ in the denominator. This means we can write ${x}^{4 - \left(- 3\right)} = {x}^{7}$ in the numerator.

We have ${y}^{- 2}$ in the numerator and ${y}^{5}$ in the denominator. This means we can write ${y}^{- 2 - 5} = {y}^{- 7}$ in the numerator.

Hence:

$\implies \frac{{x}^{4} {y}^{- 2}}{{x}^{- 3} {y}^{5}} = {x}^{7} {y}^{- 7}$

Or, equilavently:

$\implies {x}^{7} {y}^{- 7} = {x}^{7} / {y}^{7} = {\left(\frac{x}{y}\right)}^{7}$