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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584

Solutions

BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

Compare Exponential Expressions

a. How many times as large is 3 ( 3 3 ) than ( 3 3 ) 3 ?

b. How many times as large is 4 ( 4 4 ) than ( 4 4 ) 4 ? Note: Most calculators will not display the answer to this problem because it is too large. However, the answer can be determined in exponential form by applying the following properties of exponents.

( a m ) n = a m n a n d a m a n = a m n

a.

To determine

The number of times the number 3(33) is larger than (33)3 .

Explanation

Given information: The answer can be determined in exponential form by applying the following properties of exponents.

(am)n=amn and aman=amn

Calculation:

The number 3(33) is 327 and the number (33)3 is 39 .

The number 327 is 32739 times larger than 39

b.

To determine

The number of times the number 4(44) is larger than (44)4 .

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