We are asked to simplify the expression $(x^7)^{-2}$ and express the answer using a single exponent.

1. Problem Description

We are asked to simplify the expression $(x^7)^{-2}$ and express the answer using a single exponent.

2. Solution Steps

To simplify the expression $(x^7)^{-2}$, we need to use the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

In our case, we have $a = x$, $m = 7$, and $n = -2$.

Applying the power of a power rule:

$(x^7)^{-2} = x^{7 \cdot (-2)} = x^{-14}$

3. Final Answer

$x^{-14}$