The problem asks to evaluate the numerical expression $(-128)^{9/7}$.

1. Problem Description

The problem asks to evaluate the numerical expression $(-128)^{9/7}$.

2. Solution Steps

We need to evaluate $(-128)^{9/7}$. First, we can express this as $((-128)^{1/7})^9$ or $((-128)^9)^{1/7}$. It is easier to evaluate the first expression.

First, we evaluate $(-128)^{1/7}$. Since $(-2)^7 = -128$, we have

$(-128)^{1/7} = -2$.

Now, we need to evaluate $(-2)^9$. Since $2^9 = 512$, we have $(-2)^9 = -512$.

Therefore, $(-128)^{9/7} = (-2)^9 = -512$.

3. Final Answer

-512