The problem asks us to find two expressions that are equivalent to $7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7$.

1. Problem Description

The problem asks us to find two expressions that are equivalent to $7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7$.

2. Solution Steps

First, we can express $7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7$ as $7^6$. Now let's examine the given answer choices:

A. $7^6$ - This is equivalent.

B. $\frac{7^8}{7^2}$ - Using the quotient of powers rule, $\frac{a^m}{a^n} = a^{m-n}$.

So, $\frac{7^8}{7^2} = 7^{8-2} = 7^6$. This is equivalent.

C. $(7^3)^4$ - Using the power of a power rule, $(a^m)^n = a^{m \cdot n}$.

So, $(7^3)^4 = 7^{3 \cdot 4} = 7^{12}$. This is not equivalent.

D. $\frac{7^{12}}{7^2}$ - Using the quotient of powers rule, $\frac{a^m}{a^n} = a^{m-n}$.

So, $\frac{7^{12}}{7^2} = 7^{12-2} = 7^{10}$. This is not equivalent.

3. Final Answer

The equivalent expressions are $7^6$ and $\frac{7^8}{7^2}$.