# How do you divide ((x^4y^-2)/(x^-3y^5))^-1?

Jul 11, 2015

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

#### Explanation:

Step 1: Move the power outside the brackets into it:
${\left(\frac{{x}^{4} {y}^{-} 2}{{x}^{-} 3 {y}^{5}}\right)}^{-} 1 = \frac{{x}^{-} 3 {y}^{5}}{{x}^{4} {y}^{-} 2}$

Step 2: Move the denominator terms into the numerator:
$\frac{{x}^{-} 3 {y}^{5}}{{x}^{4} {y}^{-} 2} = \left({x}^{-} 3 {y}^{5}\right) \left({x}^{-} 4 {y}^{2}\right)$

Step 3: Combine similar terms:
$\left({x}^{-} 3 {y}^{5}\right) \left({x}^{-} 4 {y}^{2}\right) = {x}^{-} 7 {y}^{7} = {\left(\frac{y}{x}\right)}^{7}$