Answer
$x=-3$
Work Step by Step
The given expression is
$\Rightarrow (\frac{1}{5})^x=125$
Rewrite $\frac{1}{5}$ as $5^{-1}$ and $125=5^3$.
$\Rightarrow (5^{-1})^x=5^3$
Use $(a^n)^m=a^{n\cdot m}$
$\Rightarrow 5^{-1\cdot x}=5^{3}$
Simplify.
$\Rightarrow 5^{-x}=5^{3}$
Equate the exponents.
$\Rightarrow -x=3$
Multiply each side by $-1$.
$\Rightarrow -1(-x)=-1(3)$
Simplify.
$\Rightarrow x=-3$
Check: $(x=-3)$
$\Rightarrow (\frac{1}{5})^{-3}=125$
$\Rightarrow 5^{3}=125$
$\Rightarrow 125=125$
True.
Hence, the solution is $x=-3$.
