Question

1. rewrite $9^{-3}$ using a positive exponent.
2. what does the exponent tell you about the expression?
3. $9^{-3}$ is equal to ? factors of ?.

Explanation:

Step1: Rewrite with positive exponent

Recall the rule $a^{-n}=\frac{1}{a^n}$. For $9^{-3}$, substitute $a=9$, $n=3$:
$9^{-3}=\frac{1}{9^3}$

Step2: Interpret negative exponent

A negative exponent means we take the reciprocal, so $9^{-3}$ represents the reciprocal of 3 factors of 9, which is $\frac{1}{9}$ repeated 3 times (i.e., 3 factors of $\frac{1}{9}$).

Answer:

1. Rewritten with positive exponent: $\boldsymbol{\frac{1}{9^3}}$
2. The exponent tells you to take the reciprocal of the base raised to the positive value of the exponent.
3. $9^{-3}$ is equal to $\boldsymbol{3}$ factors of $\boldsymbol{\frac{1}{9}}$.