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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. 124 (page 786)

In the following exercises, write with a rational exponent.
$鈸� \sqrt[8]{r} 鈸� \sqrt[10]{s} 鈸� \sqrt[4]{t}$

Short Answer

Expert verified

Part (a). $\sqrt[8]{r} = r^{\frac{1}{8}}$

Part (b). role="math" localid="1644748622060" $\sqrt[10]{s} = s^{\frac{1}{10}}$

Part (c). $\sqrt[4]{t} = t^{\frac{1}{4}}$

Step by step solution

01

Part (a) Step 1. Rational exponent of r8

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $8$

The denominator of the exponent will be $8$ .

$\sqrt[8]{r} = r^{\frac{1}{8}}$

02

Part (b) Step 1. Rational exponent of s10

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $10$

The denominator of the exponent will be $10$

$\sqrt[10]{s} = s^{\frac{1}{10}}$

03

Part (c) Step 1. Rational exponent of t4

We know that, $\sqrt[n]{a} = a^{\frac{1}{n}}$

The index is $4$

The denominator of the exponent will be $4$

4 $\sqrt[4]{t} = t^{\frac{1}{4}}$

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Most popular questions from this chapter

Write with a rational exponent:

(a) $\sqrt{10 m}$

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

(c) $3 \sqrt[4]{6 y}$

Simplify:

$(a) \sqrt[3]{- 64} (b) \sqrt[4]{- 81} .$

In the following exercises, solve.

$\sqrt{3 y - 4} = - 2$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{147}$

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