# Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Lesson Check - Page 417: 5

$-2$

#### Work Step by Step

We start with the given expression: $a^3b^{-1}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. Using this rule, we rewrite the expression as: $\frac{a^3}{b}$ We plug in the given values for $a$ and $b$: $\frac{2^3}{-4}$ The order of operations states that first we perform operations inside grouping symbols, such as parentheses, brackets, and fraction bars. Then, we simplify powers. Then, we multiply and divide from left to right. We follow the order of operations to simplify: First, we simplify above the fraction bar: $\frac{8}{-4}$ Then, we divide: $-2$

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