Question

select all the expressions that are equivalent to $\frac{9^{2}}{3^{2}}$.
$3^{0}$
$3^{2}$
$\frac{3^{5}}{3^{3}}$
$3$

Explanation:

Step1: Simplify the original expression

First rewrite $9$ as $3^2$:
$$\frac{9^2}{3^2} = \frac{(3^2)^2}{3^2} = \frac{3^4}{3^2}$$
Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$$3^{4-2}=3^2=9$$

Step2: Evaluate each option

1. $3^0 = 1$ (not equal to 9)
2. $3^2 = 9$ (equal to original)
3. $\frac{3^5}{3^3}=3^{5-3}=3^2=9$ (equal to original)
4. $3$ (not equal to 9)

Answer:

B. $3^2$, C. $\frac{3^5}{3^3}$