Question

Write as a radical expression and evaluate if possible

Answer 1

Remember that $x^{\frac{m}{n}} = \sqrt[n]{x^m}$.

By this, we can say that $8^{\frac{1}{3}} = \sqrt[3]{8}$.

This evaluated is equal to 2.

Our answer is choice A, $\boxed{\sqrt[3]{8};\,2}$.

Answer 2

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------\\\\ 8^{\frac{1}{3}}\implies \sqrt[3]{8^1}\implies \sqrt[3]{8}~~ \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3 \end{cases}\implies \sqrt[3]{2^3}\implies 2$