Chapter 7 - Exponents and Exponential Functions - 7-5 Rational Exponents and Radicals - Practice and Problem-Solving Exercises - Page 451: 29

$4x^{2/3}$

Work Step by Step

$\sqrt[3]{(8x)^{2}}=\quad$... apply $\ \ \sqrt[n]{a^{m}}=a^{m/n},$ $=(8x)^{2/3}=\quad$... power of a power $=8^{2/3}\cdot x^{2/3}\quad$... recognize $8$ as $2^{3}$ $=(2^{3})^{2/3}\cdot x^{2/3}=\quad$... power of a power $= 2^{2}x^{2/3}$ = $4x^{2/3}$

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