Answer
$x=1$.
Work Step by Step
$8^{1/3}=2^{x}$
$(2^{3})^{1/3}=2^{x}$ (since $2^{3}=8$)
$(2^{3*1/3})=2^{x}$
$(2^{1})=2^{x}$
$x=1$
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