The problem asks us to simplify the expression $(3g^3 \times g^4)^5$.

1. Problem Description

The problem asks us to simplify the expression $(3g^3 \times g^4)^5$.

2. Solution Steps

First, we simplify the expression inside the parentheses:

$3g^3 \times g^4 = 3g^{3+4} = 3g^7$

Then, we raise the result to the power of 5:

$(3g^7)^5 = 3^5 \times (g^7)^5$

We know that $(a^m)^n = a^{m \times n}$, so $(g^7)^5 = g^{7 \times 5} = g^{35}$.

Also, $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$.

Therefore, $(3g^7)^5 = 243g^{35}$.

3. Final Answer

$243g^{35}$