Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Practice and Problem-Solving Exercises - Page 418: 37

$-\frac{1}{27}$

We start with the given expression: $r^{-3}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{1}{r^3}$ Next, we plug in the value for $r$: $\frac{1}{(-3)^3}$ We expand the exponent and simplify: $\frac{1}{(-3)(-3)(-3)}=-\frac{1}{27}$