Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - Chapter R Test Prep - Review Exercises: 111

Answer

$\color{blue}{66}$

Work Step by Step

RECALL: $(a+b)(a^2-ab+b^2) = a^3+b^3$ Note that: $\sqrt[3]{2^2} = (\sqrt[3]{2})^2$ $16=4^2$ Thus, if we let $a=\sqrt[3]{2}$ and $b=4$ The expression above becomes: $=(a+b)(a^2-ba+b^2)$ which is equivalent to $(a+b)(a^2-ab+b^2)$ Therefore, using the formula in the recall part above, the given expression simplifies to: $=(\sqrt[3]{2})^3+4^3 \\=2+64 \\=\color{blue}{66}$
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