Respuesta :

[tex] \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 [/tex]

qabtt

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

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

This evaluated is equal to 2.

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

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