Answer
$x=29$
Work Step by Step
Note that
$\sqrt[3]{x-2}=3 \Rightarrow(x-2)^{1 / 3}=3$
Raise both sides to the third power to eliminate the fractional exponent:
$((x-2)^\frac{1}{3})^3=3^{3}$
$(x-2)^1=27$
$x-2=27$
$x=27+2$
$x=29$
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