# The meaning of the expression 4 3 2 and calculate the value of the rational exponent 4 3 2 in two ways.

### Precalculus: Mathematics for Calcu...

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

### 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

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.

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