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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. 81 (page 771)

In the following exercises, simplify using absolute value signs as needed.
$a . \sqrt[5]{- 32} b . \sqrt[8]{- 1}$

Short Answer

Expert verified

The simplified expressions are,

$a . - 2$

b. Not a real number.

Step by step solution

01

Step 1 Given expressions are,

$a . \sqrt[5]{- 32} b . \sqrt[8]{- 1}$

The objective is, we need to find the simplified expressions for the given expressions.

The product property for the root is,

$\sqrt[n]{a b} = \sqrt[n]{a} . \sqrt[n]{b}$ and $\sqrt[n]{a} . \sqrt[n]{b} = \sqrt[n]{a b}$

02

Part a Step 2-325.

$\sqrt[5]{- 32} = \sqrt[5]{{(- 2)}^{5}} = - 2$

03

Part b Step 2 -18=-1.

Because, there is not a perfect power of the index $n$ , where $n^{8}$ is the no real number $- 1$ .

So, the answer is not a real number.

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Most popular questions from this chapter

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. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

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, write with a rational exponent.

$\sqrt[3]{7 c} 鈸� \sqrt[7]{12 d} 鈸� 2 \sqrt[4]{6 b}$

In the following exercises, write with a rational exponent.

$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

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