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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. 484 (page 851)

In the following exercises, simplify.
$(a) \sqrt[3]{- 512} (b) \sqrt[4]{- 81} (c) \sqrt[5]{- 1}$

Short Answer

Expert verified

The required answers are $- 8, 3 \sqrt[4]{- 1} a n d - 1$

Step by step solution

01

Step 1. Given Information

The given expressions are

$(a) \sqrt[3]{- 512} (b) \sqrt[4]{- 81} (c) \sqrt[5]{- 1}$

02

Part (a) Step 1. Calculation

Simplify the expression,

$\sqrt[3]{- 512} = - \sqrt[3]{512} = - \sqrt[3]{8^{3}} = - 8$

03

Part (b) Step 1. Calculation

Simplify the expression

$\sqrt[4]{- 81} = \sqrt[4]{{(- 3)}^{4}} = 3 \sqrt[4]{- 1}$

04

Part (c) Step 1. Calculation

Simplify the expression

$\sqrt[5]{- 1} = - 1$

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Most popular questions from this chapter

Simplify:

a. $\frac{u^{\frac{4}{5}} 路 u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{9}}{s^{8}}}$

(b) $\sqrt[3]{\frac{54 a^{8}}{b^{3}}}$

(c) $\sqrt[4]{\frac{64 c^{5}}{d^{4}}}$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{27}$ .

In the following exercises, simplify using absolute value signs as needed.

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Simplify: $\sqrt{\frac{24 p^{3}}{49}} .$

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