Answer
$\dfrac{1}{x^{4}}$
Work Step by Step
When we raise a power to a power, we simply multiply the two powers together:
\begin{align*}
(x^{-\frac{4}{7}})^{7}&= x^{-\frac{4}{7}({7})}\\
&=x^{-\frac{28}{7}}\\
&=x^{-4}
\end{align*}
Simplified expressions should not haven negative exponents.
To get rid of the negative exponent, use the rule $a^{-m}=\frac{1}{a^m}$ to obtain:
$$x^{-4}=\frac{1}{x^{4}}$$
