Answer
$300\sqrt[3]{3}$
Work Step by Step
Since $\sqrt[n]{a}=a^{1/n}$, we have
$$
(\sqrt[3]{3}\sqrt{10})^4=(\sqrt[3]{3})^4(\sqrt{10})^4=\sqrt[3]{3^4}\sqrt{10^4}\\
=\sqrt[3]{3(3^3)}\sqrt{10^2(10)^2}=300\sqrt[3]{3}
.$$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A60: 24
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