# How do you evaluate 5z^ -x for z=-3 and x=2?

May 8, 2017

See a solution process below:

#### Explanation:

First, substitute $\textcolor{red}{- 3}$ for $\textcolor{red}{z}$ and substitute $\textcolor{b l u e}{2}$ for $\textcolor{b l u e}{x}$ in the expression from the problem:

$5 {\textcolor{red}{z}}^{- \textcolor{b l u e}{x}}$ becomes:

$5 \cdot {\textcolor{red}{- 3}}^{- \textcolor{b l u e}{2}}$

Now, use this rule for exponents to eliminate the negative exponent:

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

$5 \cdot {\textcolor{red}{- 3}}^{- \textcolor{b l u e}{2}} \implies 5 \cdot \frac{1}{\textcolor{red}{- 3}} ^ \left(- \textcolor{b l u e}{- 2}\right) \implies 5 \cdot \frac{1}{\textcolor{red}{- 3}} ^ \left(\textcolor{b l u e}{2}\right) \implies 5 \cdot \frac{1}{9} \implies \frac{5}{9}$