# How do you simplify [4 * x * (y^ -2)] / {12 * [x^ (-1/3)] * (y^ -5)}?

Jul 2, 2016

$= \frac{{x}^{\frac{4}{3}} \cdot {y}^{3}}{3} \text{ or } \frac{\sqrt[3]{{x}^{4}} \cdot {y}^{3}}{3}$

#### Explanation:

A first step would be to simplify what we can easily and sort out the negative indices. Divide the numbers, then move the bases with the negative indices to make them positive.

$\frac{\cancel{4} \cdot x \cdot \left({y}^{-} 2\right)}{{\cancel{12}}^{3} \cdot \left[{x}^{- \frac{1}{3}}\right] \cdot \left({y}^{-} 5\right)}$

=$\frac{x \cdot {x}^{\frac{1}{3}} \cdot \left({y}^{5}\right)}{3 \cdot \left({y}^{2}\right)}$

$= \frac{{x}^{\frac{4}{3}} \cdot {y}^{3}}{3}$