Question

select all the expressions that are equivalent to $\frac{9^{-3}}{3^{-3}}$.
$3^{0}$
$3^{-6}$
$\frac{1}{3^{3}}$
$3$
submit

Explanation:

Step1: Rewrite numerator as power of 3

$9^{-3} = (3^2)^{-3} = 3^{-6}$

Step2: Simplify the fraction

$\frac{3^{-6}}{3^{-3}} = 3^{-6 - (-3)} = 3^{-3}$

Step3: Rewrite negative exponent

$3^{-3} = \frac{1}{3^3}$

Answer:

$\boldsymbol{\frac{1}{3^3}}$, $\boldsymbol{3^{-3}}$
(Note: The original checked options are incorrect. The correct equivalent expressions are $\frac{1}{3^3}$ and $3^{-3}$)