Q.Evaluate: $8^{2/3}$.

A fractional exponent $m/n$ can be evaluated by taking the $n$-th root first and then raising to the power $m$, or the other way round — both give the same result. …

Route 1 — root first, then power:

since $2\times2\times2=8$, so $\sqrt[3]{8}=2$.

Route 2 — power first, then root (independent check):

$8^{2/3} = \left(8^2\right)^{1/3} = 64^{1/3} = \sqrt[3]{64} = 4$ …

Route 2 above (power first: $64^{1/3}$) serves as the independent cross-check for Route 1 (root first: $2^2$) — choosing the root-first route is usually easier arithm …

Taking only the root and forgetting to also apply the power in the numerator (stopping at $\sqrt[3]{8}=2$ instead of squaring it to get $4$), or attempting the power-first route with numbers …