Answer
$x=-7$
Check:
$2^{x}=2^{-7}=\frac{1}{2^{7}}=\frac{1}{128}$ which is true.
Work Step by Step
$2^{x}=\frac{1}{128}$
$\implies 2^{x}=\frac{1}{2^{7}}$
$\implies 2^{x}=2^{-7}$
$\implies x=-7$
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