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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 543RE (page 854)

In the following exercise, solve $(8 x + 5)^{\frac{1}{3}} + 2 = - 1$

Short Answer

Expert verified

Solution is $x = - 4$

Step by step solution

01

Given information

Solve $(8 x + 5)^{\frac{1}{3}} + 2 = - 1$

02

Solution

We have

$(8 x + 5)^{\frac{1}{3}} + 2 = - 1 (8 x + 5)^{\frac{1}{3}} = - 3 (8 x + 5) = {(- 3)}^{3} 8 x + 5 = - 27 8 x = - 32 x = \frac{- 32}{8} x = - 4$

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Most popular questions from this chapter

Simplify $\sqrt{45}$

Write with a rational exponent:

(a) $\sqrt[5]{a^{2}}$

(b) ${(\sqrt[3]{5 a b})}^{5}$

(c) $\sqrt{{(\frac{7 x y}{z})}^{3}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{80 q^{5}}}{\sqrt{5 q}}$

(b) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$

(c) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

Explain what is meant by the $n^{t h}$ root of a number.

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[4]{32}$ ,b. $\sqrt[5]{64}$

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