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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 257 (page 810)

In the following exercises, simplify.
$\frac{\sqrt[3]{48 a^{3} b^{6}}}{\sqrt[3]{3 a^{- 1} b^{3}}}$

Short Answer

Expert verified

The simplified form is $2 a b^{3} \sqrt{2 a}$ .

Step by step solution

01

Step 1. Given information.

The given expression is

$\frac{\sqrt[3]{48 a^{3} b^{6}}}{\sqrt[3]{3 a^{- 1} b^{3}}}$ .

02

Step 2. Simplifying.

Now, to simplify the expression first we will rewrite the expression using the quotient property.

$\frac{\sqrt[3]{48 a^{3} b^{6}}}{\sqrt[3]{3 a^{- 1} b^{3}}} = \sqrt[3]{\frac{48 a^{3} b^{6}}{3 a^{- 1} b^{3}}}$

Then removing the common factors.

$\sqrt[3]{\frac{48 a^{3} b^{6}}{3 a^{- 1} b^{3}}} = \sqrt[3]{16 a^{4} b^{3}}$

On simplifying we get,

$\sqrt[3]{16 a^{4} b^{3}} = 2 a b^{3} \sqrt{2 a}$

Hence, the simplified form is $2 a b^{3} \sqrt{2 a}$ .

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