BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.2, Problem 4E
To determine

To explain: The meaning of the expression 432 and calculate the value of the rational exponent 432 in two ways.

Expert Solution

Answer to Problem 4E

The value of rational exponent 432 is 8 and the two ways of expressing the expression 432 are 432=(412)3_ and 432=(43)12_.

Explanation of Solution

Definition used:

Definition of rational exponents:

“For any rational exponent mn in its lowest terms, where m and n are integers and n>0 we define, (a)mn=(a)mn=(an)m”.

Calculation:

The given expression is 432.

Note that, the given expression 432 is an exponential expression with base 4 and the exponent 32.

Use the above definition and write the expression 432 as 432=(412)3.

Now, simplify the above obtained expression as follows.

(412)3=((22)12)3=23                           (am1n=amn)=8

Thus, the value of expression (412)3 is 8.

Note that, the expression 432 can also be expressed as 432=(43)12.

Now, simplify the expression 432=(43)12 as shown below.

(43)12=((64)12)=(82)12=8                    (am1n=amn)

Thus, the value of expression (43)12 is 8.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!