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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. 8.52 (page 775)

Write as a radical expression:
(a) $b^{\frac{1}{6}}$
(b) $z^{\frac{1}{5}}$
(c) $p^{\frac{1}{4}}$

Short Answer

Expert verified

The radical expression of $b^{\frac{1}{6}}$ is $\sqrt[6]{b}$ .

The radical expression of $z^{\frac{1}{5}}$ is $\sqrt[5]{z}$ .

The radical expression of $p^{\frac{1}{4}}$ is $\sqrt[4]{p}$ .

Step by step solution

01

Part (a) Step 1. Given

The expression $b^{\frac{1}{6}}$

To write the given expression in the form of $\sqrt[n]{a}$

02

Part (a) Step 2. Write as rational expression

The denominator of rational exponent is $6$ , so the index of the radical is $6$ .

The radical expression is $\sqrt[6]{b}$

03

Part (b) Step 1. Given

The expression $z^{\frac{1}{5}}$

To write the given expression in the form of $\sqrt[n]{a}$

04

Part (b) Step 2. Write as rational expression

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

The radical expression is $\sqrt[5]{z}$

05

Part (c) Step 1. Given

The expression $p^{\frac{1}{4}}$

To write the given expression in the form of $\sqrt[n]{a}$

06

Part (c) Step 2. Write as rational expression

The denominator of the exponent is $4$ , so the index is $4$ .

The radical expression is $\sqrt[4]{p}$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt{4 m + 2} + 2 = 6$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

Explain how you know that

$\sqrt[5]{x^{10}} = x^{2}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Simplify:

(a) $4^{\frac{3}{2}}$

(b) $27^{- \frac{2}{3}}$

(c) $625^{- \frac{3}{4}}$

See all solutions

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