Answer
$x=7$
Work Step by Step
$5^{4-x}=\dfrac{1}{125}$
Rewrite $125$ as $5^{3}$:
$5^{4-x}=\dfrac{1}{5^{3}}$
Take $5^{3}$ to the numerator by changing the sign of its exponent:
$5^{4-x}=5^{-3}$
If $5^{4-x}=5^{-3}$, then $4-x=-3$
$4-x=-3$
Solve for $x$:
$-x=-3-4$
$-x=-7$
$x=7$
