# How do you simplify (x ^ { - 2} y ^ { 0} z ) ^ { - 3}?

Mar 1, 2017

See the entire simplification process below:

#### Explanation:

First, use these rules of exponents to simplify the exponent outside the parenthesis:

$a = {a}^{\textcolor{red}{1}}$ and $a = {a}^{\textcolor{red}{1}}$

${\left({x}^{-} 2 {y}^{0} z\right)}^{-} 3 = {\left({x}^{\textcolor{red}{- 2}} {y}^{\textcolor{red}{0}} {z}^{\textcolor{red}{1}}\right)}^{\textcolor{b l u e}{- 3}} = {x}^{\textcolor{red}{- 2} \times \textcolor{b l u e}{- 3}} {y}^{\textcolor{red}{0} \times \textcolor{b l u e}{- 3}} {z}^{\textcolor{red}{1} \times \textcolor{b l u e}{- 3}} =$

${x}^{6} {y}^{0} {z}^{-} 3$

We can now use this rule of exponents to eliminate the $y$ term:

${a}^{\textcolor{red}{0}} = 1$

${x}^{6} {y}^{\textcolor{red}{0}} {z}^{-} 3 = {x}^{6} \times 1 \times {z}^{-} 3 = {x}^{6} {z}^{-} 3$

If we want to eliminate all negative exponents we can now use this rule of exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${x}^{6} {z}^{\textcolor{red}{- 3}} = {x}^{6} / {z}^{\textcolor{red}{- - 3}} = {x}^{6} / {z}^{3}$