Question

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

Explanation:

Step1: Rewrite base 9 as power of 3

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

Step2: Simplify the fraction

$\frac{3^{-6}}{3^{-6}} = 3^{-6 - (-6)} = 3^{0}$

Step3: Evaluate $3^0$ and rewrite

$3^0 = 1$, and $\frac{1}{3^0} = \frac{1}{1} = 1$

Answer:

$3^0$, $\frac{1}{3^0}$