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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q581 (page 857)

Simplify using absolute values as necessary.
$\sqrt[3]{72 x^{8} y^{4}}$

Short Answer

Expert verified

The Solution is $2 x^{2} y \sqrt[3]{9 x^{2} y}$

Step by step solution

01

The Given Information

An expression is $\sqrt[3]{72 x^{8} y^{4}}$

02

Simplifying

$= \sqrt[3]{72 x^{8} y^{4}} \sqrt[3]{72} \Rightarrow \sqrt[3]{8.9} \Rightarrow 2 \sqrt[3]{9} \sqrt[3]{x^{8}} \Rightarrow \sqrt[3]{x^{6} . x^{2}} \Rightarrow x^{2} \sqrt[3]{x^{2}} \sqrt[3]{y^{4}} \Rightarrow \sqrt[3]{y^{3} . y} \Rightarrow y \sqrt[3]{y} = 2 x^{2} y \sqrt[3]{9 x^{2} y}$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt[3]{6 x + 4} = 4$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

Simplify-

(a) $\sqrt{288}$

(b) $\sqrt[3]{81}$

(c) $\sqrt[4]{64}$

In the following exercises, write as a radical expression.

$ⓐ u^{\frac{1}{5}} ⓑ v^{\frac{1}{9}} ⓒ w^{\frac{1}{20}}$

Simplify::
(a) $100^{\frac{1}{2}}$

(b) $27^{\frac{1}{3}}$

(c) $81^{\frac{1}{4}}$

See all solutions

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