Chapter 8: Q. 8.41 (page 765)

Simplify:
$(a) \sqrt{\frac{a^{8}}{a^{6}}} (b) \sqrt[4]{\frac{x^{7}}{x^{3}}} (c) \sqrt[4]{\frac{y^{17}}{y^{5}}}$

Short Answer

Expert verified

Part a. After simplifying we get, $a .$

Part b. After simplifying we get, $x .$

Part c. After simplifying we get, $y^{3} .$

Step by step solution

Part a Step 1. Given Information

The given expression is $\sqrt{\frac{a^{8}}{a^{6}}} .$

We have to simplify it.

Part a Step 2. Use the Quotient Property of exponents to simplify

By using the property we get,

$\sqrt{\frac{a^{8}}{a^{6}}} = \sqrt{a^{8 - 6}} = \sqrt{a^{2}} = a$

Part b Step 1. Given Information

The given expression is $\sqrt[4]{\frac{x^{7}}{x^{3}}} .$

We have to simplify it.

Part b Step 2. Use the Quotient Property of exponents to simplify

By using the property we get,

$\sqrt[4]{\frac{x^{7}}{x^{3}}} = \sqrt[4]{x^{7 - 3}} = \sqrt[4]{x^{4}} = x$

Part c Step 1. Given Information

The given expression is $\sqrt[4]{\frac{y^{17}}{y^{5}}} .$

We have to simplify it.

Part c Step 2. Use the Quotient Property of exponents to simplify

By using the property we get,

$\sqrt[4]{\frac{y^{17}}{y^{5}}} = \sqrt[4]{y^{17 - 5}} = \sqrt[4]{y^{12}} = \sqrt[4]{{(y^{3})}^{4}} = y^{3}$

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Simplify:
$(a) \sqrt{\frac{a^{8}}{a^{6}}} (b) \sqrt[4]{\frac{x^{7}}{x^{3}}} (c) \sqrt[4]{\frac{y^{17}}{y^{5}}}$

Short Answer

Step by step solution

Part a Step 1. Given Information

Part a Step 2. Use the Quotient Property of exponents to simplify

Part b Step 1. Given Information

Part b Step 2. Use the Quotient Property of exponents to simplify

Part c Step 1. Given Information

Part c Step 2. Use the Quotient Property of exponents to simplify

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Simplify:aa8a6bx7x34cy17y54

Short Answer

Step by step solution

Part a Step 1. Given Information

Part a Step 2. Use the Quotient Property of exponents to simplify

Part b Step 1. Given Information

Part b Step 2. Use the Quotient Property of exponents to simplify

Part c Step 1. Given Information

Part c Step 2. Use the Quotient Property of exponents to simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \sqrt{\frac{a^{8}}{a^{6}}} (b) \sqrt[4]{\frac{x^{7}}{x^{3}}} (c) \sqrt[4]{\frac{y^{17}}{y^{5}}}$