Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Practice and Problem-Solving Exercises - Page 417: 11

$\frac{1}{25}$

We want to simplify: $(-5)^{-2}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this to rewrite the expression as $\frac{1}{(-5)^2}$. Next, we must simplify the power on the denominator: $\frac{1}{-5\times-5}=\frac{1}{25}$