The problem asks us to select the three expressions that are equivalent to $6^2$.

1. Problem Description

The problem asks us to select the three expressions that are equivalent to $6^2$.

2. Solution Steps

We need to evaluate each expression and see if it is equal to $6^2 = 36$.

A. $\left(\frac{6^9}{6^8}\right)^2 = (6^{9-8})^2 = (6^1)^2 = 6^2 = 36$. This is equivalent to $6^2$.

B. $\frac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6} = \frac{6^6}{6^3} = 6^{6-3} = 6^3 = 216$. This is not equivalent to $6^2$.

C. $\frac{6^4}{6^2} = 6^{4-2} = 6^2 = 36$. This is equivalent to $6^2$.

D. $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 2^6 = 64$. This is not equivalent to $6^2$.

E. $\frac{6^5 \cdot 6^7}{6^{10}} = \frac{6^{5+7}}{6^{10}} = \frac{6^{12}}{6^{10}} = 6^{12-10} = 6^2 = 36$. This is equivalent to $6^2$.

The expressions equivalent to $6^2$ are A, C, and E.

3. Final Answer

A, C, E