The problem asks us to simplify the expression $(\frac{2h^{13}}{h^8})^4$.

1. Problem Description

The problem asks us to simplify the expression $(\frac{2h^{13}}{h^8})^4$.

2. Solution Steps

First, we simplify the expression inside the parentheses. When dividing exponents with the same base, we subtract the exponents.

$\frac{h^{13}}{h^8} = h^{13-8} = h^5$

So, the expression becomes:

$(\frac{2h^{13}}{h^8})^4 = (2h^5)^4$

Now, we apply the power of a product rule, which states that $(ab)^n = a^n b^n$.

$(2h^5)^4 = 2^4 (h^5)^4$

$2^4 = 2 \times 2 \times 2 \times 2 = 16$

When raising a power to another power, we multiply the exponents.

$(h^5)^4 = h^{5 \times 4} = h^{20}$

Putting it all together:

$2^4 (h^5)^4 = 16h^{20}$

3. Final Answer

The final answer is $16h^{20}$.