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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. 227 (page 799)

Simplify:
$8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

Short Answer

Expert verified

The value of the given expression is $17 q^{2}$ .

Step by step solution

01

Step 1. Given information

The given expression is $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

02

Step 2. Simplifying the expression

Simplifying the radicals, we get:

$8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}} 8 \sqrt[3]{{(4 q^{2})}^{3}} - 3 \sqrt[3]{{(5 q^{2})}^{3}} 8 路 4 q^{2} - 3 路 5 q^{2} [\sqrt[3]{64 q^{2}} = 4 q^{2}, \sqrt[3]{125 q^{6}} = 5 q^{2}] 32 q^{2} - 15 q^{2}$

Subtracting the like radicals, we get:

$32 q^{2} - 15 q^{2} 17 q^{2}$

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Most popular questions from this chapter

Simplify:

a. $x^{\frac{1}{6}} 路 x^{\frac{4}{3}}$ b. ${(x^{6})}^{\frac{4}{3}}$ c. $\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}}$

Write with a rational exponent:

(a) $\sqrt[7]{3 k}$

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In the following exercises, solve.
$\sqrt{2 u - 3} + 2 = 0$

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