Answer
$4\sqrt[3]{d^{2}}$
Work Step by Step
$(8d)^{\frac{2}{3}}\qquad$...write in radical form, $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$
$=\sqrt[3]{(8d)^{2}}$
$=\sqrt[3]{64d^{2}}\qquad$...recognize $64$ as the third power of $4$.
$=\sqrt[3]{4^{3}d^{2}}\qquad$...apply radical rule:$\sqrt[n]{a^{n}}=a$
$=4\sqrt[3]{d^{2}}$
