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Q18.

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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. (5)3

b. role="math" localid="1648704247043" 53

c. (5)2(25)2

a) The value of (5)3 is 125.

b) The value of 53 is 125.

c) The value of (5)2(25)2 is 4.

See the step by step solution

Step by Step Solution

Part a Step 1. Given information. 

The given expression is (5)3.

Part a  Step 2. Write the concept.

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:

(5)3=(5)×(5)×(5)=125

Thus, the value of (5)3 is 125.

Part b Step 1. Given information.

The given expression is 53.

Part b  Step 2. Write the concept.

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:

53=(5×5×5)=125

Thus, the value of 53 is 125.

Part c Step 1. Given information.

The given expression is (5)2252.

Part c  Step 2. Write the concept.

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:

(5)2252=(5)×(5)×25×25=(25)×425=4

Thus, the value of (5)2252 is 4.

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