Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 9 - Solving Quadratic Equations - 9.1 - Properties of Radicals - Exercises - Page 485: 36

Answer

$-\frac{\sqrt[3]{21}}{4ab^2}$

Work Step by Step

The given expression is $=\sqrt[3]{\frac{21}{-64a^3b^6}}$ Use quotient property of cube roots. $=\frac{\sqrt[3]{21}}{\sqrt[3]{-64a^3b^6}}$ Use product property of cube roots. $=\frac{\sqrt[3]{21}}{\sqrt[3]{-64}\cdot \sqrt[3]{a^3}\cdot \sqrt[3]{b^6}}$ Use $-64=(-4)^3$ and $b^6=(b^2)^3$. $=\frac{\sqrt[3]{21}}{\sqrt[3]{(-4)^3}\cdot \sqrt[3]{a^3}\cdot \sqrt[3]{(b^2)^3}}$ Simplify. $=\frac{\sqrt[3]{21}}{-4ab^2}$ $=-\frac{\sqrt[3]{21}}{4ab^2}$
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