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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. 8.95 (page 803)

Simplify:
(a) $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$
(b) $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$ is $\frac{9 x^{2}}{y^{2}}$

The simplification of $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$ is $\frac{4 x}{y}$

Step by step solution

01

Part (a) Step 1. Given

An expression $\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}$

To simplify the expression

02

Part (a) Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}} = \sqrt{\frac{162 x^{10} y^{2}}{2 x^{6} y^{6}}}$

Remove the common factors.

$= \sqrt{\frac{81 x^{4}}{y^{4}}}$

03

Part (a) Step 3. Simplify the expression

$\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}} = \sqrt{\frac{81 x^{4}}{y^{4}}}$

$= \sqrt{\frac{9^{2} {(x^{2})}^{2}}{{(y^{2})}^{2}}}$

$= \frac{9 x^{2}}{y^{2}}$

The simplification of the expression is $\frac{9 x^{2}}{y^{2}}$

04

Part (b) Step 1. Given

An expression $\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}}$

To simplify the expression

05

Part (b) Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}} = \sqrt[3]{\frac{128 x^{2} y^{- 1}}{2 x^{- 1} y^{2}}}$

Remove the common factors.

$= \sqrt[3]{\frac{64 x^{3}}{y^{3}}}$

06

Part (b) Step 3. Simplify the expression

$\frac{\sqrt[3]{128 x^{2} y^{- 1}}}{\sqrt[3]{2 x^{- 1} y^{2}}} = \sqrt[3]{\frac{64 x^{3}}{y^{3}}}$

$= \sqrt[3]{\frac{4^{3} x^{3}}{y^{3}}}$

$= \frac{4 x}{y}$

The simplification of the expression is $\frac{4 x}{y}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{9}}{s^{8}}}$

(b) $\sqrt[3]{\frac{54 a^{8}}{b^{3}}}$

(c) $\sqrt[4]{\frac{64 c^{5}}{d^{4}}}$

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, solve.

$\sqrt[3]{2 x} = - 2$

In the following exercises, solve.

$\sqrt{4 x - 3} = 7$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{m^{13}}, \sqrt[5]{u^{7}}, \sqrt[6]{v^{11}}$

See all solutions

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