# How do you simplify ((-3x^-6y^-1z^-2)/(6x^-2yz^-5))^-2?

Apr 30, 2017

See below.

#### Explanation:

We know that when there is a negative we flip the expression (i.e, ${x}^{-} 1 = \frac{1}{x}$).

Let's do that for this expression first.

${\left(\frac{- 3 {x}^{-} 6 {y}^{-} 1 {z}^{-} 2}{6 {x}^{-} 2 y {z}^{-} 5}\right)}^{-} 2$

${\left(\frac{- 3 {x}^{2} {z}^{5}}{6 {x}^{6} {y}^{2} {z}^{2}}\right)}^{-} 2$

Now we simplify like terms.

${\left(\frac{- {z}^{3}}{{x}^{4} {y}^{2}}\right)}^{-} 2$

Since the expression is to the $- 2$, we again flip everything.

${\left(\frac{{x}^{4} {y}^{2}}{- {z}^{3}}\right)}^{2}$

Now we square each term.

$\frac{{x}^{8} {y}^{4}}{{z}^{6}}$