Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.50 (page 770)

Simplify:
$(a) \frac{\sqrt{128 m^{9}}}{\sqrt{2 m}} (b) \frac{\sqrt[3]{- 192}}{\sqrt[3]{3}} (c) \frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $8 m^{4} .$

Part b. After simplifying we get, $- 4 .$

Part c. After simplifying we get, $3 n \sqrt[4]{2} .$

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt{128 m^{9}}}{\sqrt{2 m}}$

By using the property we can write as $\sqrt{\frac{128 m^{9}}{2 m}} .$

Part a Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt{\frac{128 m^{9}}{2 m}} = \sqrt{64 m^{9 - 1}} = \sqrt{{(8 m^{4})}^{2}} = 8 m^{4}$

Part b Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[3]{- 192}}{\sqrt[3]{3}}$

By using the property we can write as $\sqrt[3]{\frac{- 192}{3}} .$

Part b Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[3]{\frac{- 192}{3}} = \sqrt[3]{- 64} = \sqrt[3]{- {(4)}^{3}} = - 4$

Part c Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}}$

By using the property we can write as $\sqrt[4]{\frac{324 n^{7}}{2 n^{3}}} .$

Part c Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[4]{\frac{324 n^{7}}{2 n^{3}}} = \sqrt[4]{162 n^{7 - 3}} = \sqrt[4]{162 n^{4}} = \sqrt[4]{{(3 n)}^{4}} 路 \sqrt[4]{2} = 3 n \sqrt[4]{2}$

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91影视

Simplify:
$(a) \frac{\sqrt{128 m^{9}}}{\sqrt{2 m}} (b) \frac{\sqrt[3]{- 192}}{\sqrt[3]{3}} (c) \frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}} .$

Short Answer

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Part a Step 2: Simplify the fraction under the radical

Part b Step 1. Use the Quotient property to write as one radical

Part b Step 2: Simplify the fraction under the radical

Part c Step 1. Use the Quotient property to write as one radical

Part c Step 2: Simplify the fraction under the radical

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91影视

Simplify:a128m92mb-192333c324n742n34.

Short Answer

Step by step solution

Part a Step 1. Use the Quotient property to write as one radical

Part a Step 2: Simplify the fraction under the radical

Part b Step 1. Use the Quotient property to write as one radical

Part b Step 2: Simplify the fraction under the radical

Part c Step 1. Use the Quotient property to write as one radical

Part c Step 2: Simplify the fraction under the radical

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Geometry

Applied Mathematics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \frac{\sqrt{128 m^{9}}}{\sqrt{2 m}} (b) \frac{\sqrt[3]{- 192}}{\sqrt[3]{3}} (c) \frac{\sqrt[4]{324 n^{7}}}{\sqrt[4]{2 n^{3}}} .$