Simplify the expression $(v^2)^{-4}$ and express the answer using a single exponent.

1. Problem Description

Simplify the expression $(v^2)^{-4}$ and express the answer using a single exponent.

2. Solution Steps

To simplify the expression $(v^2)^{-4}$, we use the power of a power rule, which states that $(a^m)^n = a^{m \times n}$.

In this case, $a = v$, $m = 2$, and $n = -4$.

Therefore, $(v^2)^{-4} = v^{2 \times (-4)}$.

$2 \times (-4) = -8$.

So, $(v^2)^{-4} = v^{-8}$.

3. Final Answer

$v^{-8}$