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Q22.

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Precalculus Mathematics for Calculus
Found in: Page 266
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

Radicals and Exponents Evaluate each expression.

a. 38⋅35

b. 107104

c. (35)4

a) The value of38⋅35is 1594323.

b) The value of 107104 islocalid="1648708601105" 1000.

c) The value oflocalid="1648707916158" 354is3486784401.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Part a Step 1. Given information.

The given expression is 38⋅35.

Part a Step 2. Write the concept.

According to the property of exponent:

am⋅an=am+n

The exponential expression “a to the power n” is defined as:

an=a×a×a×⋯×a (n times)

Part a Step 3. Determine the value of the expression.

The given expression can be written as:

38⋅35=38+5=313=3×3×3×3×3×3×3×3×3×3×3×3×3=1594323

Thus, the value of 38⋅35 is 1594323.

Part b Step 1. Given information.

The given expression is 107104.

Part b Step 2. Write the concept.

According to the property of exponent:

aman=am−n

The exponential expression “a to the power n” is defined as:

an=a×a×a×⋯×a (n times)

Part b Step 3. Determine the value of the expression.

The given expression can be written as:

107104=107−4=103=10×10×10=1000

Thus, the value of 107104 is 1000.

Part c Step 1. Given information.

The given expression is 354.

Part c Step 2. Write the concept.

According to the property of exponent:

(am)n=amn

The exponential expression “a to the power n” is defined as:

an=a×a×a×⋯×a (n times)

Part c Step 3. Determine the value of the expression.

The given expression can be written as:

(35)4=35×4=320=3×3×3×3×3×3×3×3×3×3×3×3×3×3×3×3×3×3×3×3=3486784401

Thus, the value of 354 is 3486784401.

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