# How do you simplify (x^-1y^-2)/z^-3?

Mar 25, 2018

${z}^{3} / \left(x {y}^{2}\right)$

#### Explanation:

${x}^{-} 2 = \frac{1}{x} ^ 2$

$\frac{1}{x} ^ - 2 = {x}^{2} / 1 = {x}^{2}$

Switch the places (numerator vs denominator) of the negative exponents

$\frac{{x}^{-} 1 {y}^{-} 2}{z} ^ - 3$

${z}^{3} / \left(x {y}^{2}\right)$

Mar 25, 2018

$\implies \frac{{z}^{3}}{x {y}^{2}}$

#### Explanation:

Technically, this is already simplified to some extent. There are no like-terms that can be combined.

However, if you would like to write this in terms of only positive powers, then:

$\frac{{x}^{- 1} {y}^{- 2}}{{z}^{- 3}} \implies \frac{{z}^{3}}{x {y}^{2}}$

Negative powers keep the same power, but can be rewritten as positive if placed in the opposite part of the fraction. So a negative power in the numerator is equivalent to a positive power in the denominator, and vice-versa.