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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. 122 (page 786)

In the following exercises, write as a radical expression.
$鈸� g^{\frac{1}{7}} 鈸� h^{\frac{1}{5}} 鈸� j^{\frac{1}{25}}$

Short Answer

Expert verified

Part (a). $g^{\frac{1}{7}} = \sqrt[7]{g}$

Part (b). $h^{\frac{1}{5}} = \sqrt[5]{h}$

Part (c). $j^{\frac{1}{25}} = \sqrt[25]{j}$

Step by step solution

01

Part (a) Step 1. Radical expression of g17

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

The denominator of the rational exponent is $7$ , so the index of the radical is $7$ . We do not show the

index when it is $7$ .

$g^{\frac{1}{7}} = \sqrt[7]{g}$

02

Part (b). Radical expression of h15

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

The denominator of the exponent is $5$ , so the index is $5$ .

$h^{\frac{1}{5}} = \sqrt[5]{h}$

03

Part (c) Radical expression of j125

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

The denominator of the exponent is $25$ , so the index is $25$ .

$j^{\frac{1}{25}} = \sqrt[25]{j}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{28 q^{6}}{225}}$

Write as a radical expression:

(a) $t^{\frac{1}{2}}$

(b) $m^{\frac{1}{3}}$

(c) $r^{\frac{1}{4}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

In the following exercises, write with a rational exponent.

$鈸� \sqrt[8]{r} 鈸� \sqrt[10]{s} 鈸� \sqrt[4]{t}$

In the following exercises, solve.
$\sqrt{s - 8} = s - 8$

See all solutions

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