Chapter 8: Q. 8.42 (page 765)

Simplify:
$(a) \sqrt{\frac{x^{14}}{x^{10}}} (b) \sqrt[3]{\frac{m^{13}}{m^{7}}} (c) \sqrt[5]{\frac{n^{12}}{n^{2}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $x^{2} .$

Part b. After simplifying we get, $m^{2} .$

Part c. After simplifying we get, $n^{2} .$

Step by step solution

Part a Step 1. Given Information

The given expression is $\sqrt{\frac{x^{14}}{x^{10}}} .$

We have to simplify it.

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

By using the property we get,

$\sqrt{\frac{x^{14}}{x^{10}}} = \sqrt{x^{14 - 10}} = \sqrt{x^{4}} = \sqrt{{(x^{2})}^{2}} = x^{2}$

Part b Step 1. Given Information

The given expression is $\sqrt[3]{\frac{m^{13}}{m^{7}}} .$

We have to simplify it.

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

By using the property we get,

\sqrt[3]{\frac{m^{13}}{m^{7}}} = \sqrt[3]{m^{13 - 7}} = \sqrt[3]{m^{6}} = \sqrt[3]{{(m^{2})}^{3}} = m^{2}

Part c Step 1. Given Information

The given expression is $\sqrt[5]{\frac{n^{12}}{n^{2}}} .$

We have to simplify it.

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

By using the property we get,

$\sqrt[5]{\frac{n^{12}}{n^{2}}} = \sqrt[5]{n^{12 - 2}} = \sqrt[5]{n^{10}} = \sqrt[5]{{(n^{2})}^{5}} = n^{2}$

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Simplify:
$(a) \sqrt{\frac{x^{14}}{x^{10}}} (b) \sqrt[3]{\frac{m^{13}}{m^{7}}} (c) \sqrt[5]{\frac{n^{12}}{n^{2}}} .$

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:ax14x10bm13m73cn12n25.

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

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Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \sqrt{\frac{x^{14}}{x^{10}}} (b) \sqrt[3]{\frac{m^{13}}{m^{7}}} (c) \sqrt[5]{\frac{n^{12}}{n^{2}}} .$