The problem asks to simplify the expression $(y^{-7k})^{4}$ and express the answer using a single exponent.

1. Problem Description

The problem asks to simplify the expression $(y^{-7k})^{4}$ and express the answer using a single exponent.

2. Solution Steps

We need to use the power of a power rule which states that $(a^m)^n = a^{m \cdot n}$. In our case, $a = y$, $m = -7k$, and $n = 4$. Therefore,

$(y^{-7k})^{4} = y^{-7k \cdot 4} = y^{-28k}$.

3. Final Answer

$y^{-28k}$