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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 117 (page 773)

Explain how you know that
$\sqrt[5]{x^{10}} = x^{2}$

Short Answer

Expert verified

Thus, $\sqrt[5]{x^{10}} = x^{2}$ . Hence proved.

Step by step solution

01

Step 1. Given information.

Given expression,

$\sqrt[5]{x^{10}}$ .

02

Step 2. Write the concept.

For a given expression, there will exist largest factor in the radical that is a perfect power of index. Now, use the product rule and rewrite the radical as product of two radical.

Also, simplify the root of perfect power.

03

Step 3. Calculation.

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

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

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

In the following exercises, write with a rational exponent.

$ⓐ \sqrt[7]{x} ⓑ \sqrt[9]{y} ⓒ \sqrt[5]{f}$

In the following exercises, solve.

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

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, use the Product Property to simplify radical expression $\sqrt{27}$ .

See all solutions

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