The problem asks to find the equivalent expression of $(3^2 \cdot 5)^3$.

1. Problem Description

The problem asks to find the equivalent expression of $(3^2 \cdot 5)^3$.

2. Solution Steps

To solve this problem, we need to use the power of a product rule, which states that $(ab)^n = a^n b^n$.

Also, we need to use the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

Applying the power of a product rule to the given expression $(3^2 \cdot 5)^3$, we have:

$(3^2 \cdot 5)^3 = (3^2)^3 \cdot 5^3$

Now, we apply the power of a power rule to $(3^2)^3$:

$(3^2)^3 = 3^{2 \cdot 3} = 3^6$

Substituting this back into the expression, we get:

$(3^2 \cdot 5)^3 = 3^6 \cdot 5^3$

3. Final Answer

$3^6 \cdot 5^3$

Therefore, the correct answer is B. $3^6 \cdot 5^3$