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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. 30 (page 755)

In the following exercises, simplify using absolute values as necessary.
$鈸� \sqrt[8]{k^{8}} 鈸� \sqrt[6]{p^{6}}$

Short Answer

Expert verified

Part(a) $\sqrt[8]{k^{8}} = |k|$

Part(b) $\sqrt[6]{p^{6}} = |p|$

Step by step solution

01

Part(a) Step 1. Given information

$鈸� \sqrt[8]{k^{8}}$

Simplify using absolute values as necessary.

02

Step 2. Explanation

$\begin{array}{l} Sincetheindexniseven, \sqrt[n]{a^{n}} = |a| . \\ Heren=8isanevennumber \\ \sqrt[8]{k^{8}} = |k| \end{array}$

03

Part(b) Step 1. Given information

$鈸� \sqrt[6]{p^{6}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

$\begin{array}{l} Weusetheabsolutevaluetobesuretogetthepositiveroot. \\ Sincetheindexniseven, \sqrt[n]{a^{n}} = |a| . \\ Heren=6isanevennumber \\ \sqrt[6]{p^{6}} = |p| \end{array}$

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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) $\sqrt{\frac{45 r^{3}}{s^{10}}}$

(b) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

(c) $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

In the following exercises, write with a rational exponent.

$鈸� \sqrt[7]{x} 鈸� \sqrt[9]{y} 鈸� \sqrt[5]{f}$

Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

Write as a radical expression:

(a) $b^{\frac{1}{6}}$

(b) $z^{\frac{1}{5}}$

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

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