Chapter 6 - Exponential Functions and Sequences - 6.1 - Properties of Exponents - Monitoring Progress - Page 292: 3

$-4$

$$\begin{align*} \displaystyle \frac{-5^{0}}{2^{-2}}& =\displaystyle \frac{-(\boxed{5^{0}})}{2^{-2}} \\ &\small\text{For any nonzero number $a$, the number $a^{0}=1$.} \\ &=\displaystyle \frac{-1}{2^{-2}} \\ &\small\text{For any integer $n$ and any nonzero number $a$, the number $a^{-n}$ is the reciprocal of $a^{n}$.} \\ &=\displaystyle \frac{-1}{\left (\frac{1}{2^{2}}\right)} \\ &=\displaystyle \frac{-1}{\frac{1}{4}}\\ &=-1\displaystyle \div\frac{1}{4} \\ &=-1\displaystyle \times\frac{4}{1} \\ &=-4 \end{align*}$$