Sample Solution from
Single Variable Calculus: Early Transcendentals, Volume I
8th Edition
ISBN: 9781305270343
Chapter T
Problem 1ADT
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Textbook Problem

Evaluate each expression without using a calculator.

  1. (a) (−3)4
  2. (b) −34
  3. (c) 3−4
  4. (d) 5 23 5 21
  5. (e) ( 2 3 ) 2
  6. (f) 16−3/4

Expert Solution

(a)

To determine

To evaluate: The value of (3)4.

Answer

The value of (3)4 is 81.

Explanation of Solution

Consider the given expression (3)4.

Since the power is 4, multiply −3 four times to compute the value of (3)4.

(3)4=(3)×(3)×(3)×(3)=9×9=81

Thus, the value of (3)4 is 81.

Expert Solution

(b)

To determine

To evaluate: The value of 34.

Answer

The value of 34 is 81.

Explanation of Solution

Consider the given expression 34.

Since the power is 4, multiply 3 four times to compute the value of 34.

34=(3)×(3)×(3)×(3)=9×9=81

Thus, the value of 34 is 81.

Expert Solution

(c)

To determine

To evaluate: The value of 34.

Answer

The value of 34 is 181.

Explanation of Solution

Consider the given expression 34.

Since the power is 4 , multiply 13 four times to compute the value of 34.

34=(13)×(13)×(13)×(13)=19×19=181

Thus, the value of 34 is 181.

Expert Solution

(d)

To determine

To evaluate: The value of 523521.

Answer

The value of 523521 is 25.

Explanation of Solution

Formula used:

The a is real number and m, n are natural numbers then aman=amn.

Calculation:

Consider the given expression 523521.

Use the above mentioned formula compute the value of 523521.

523521=52321=52=25

Thus, the value of 523521 is 25.

Expert Solution

(e)

To determine

To evaluate: The value of (23)2.

Answer

The value of (23)2 is 94.

Explanation of Solution

Consider the given expression (23)2.

Since the power is 2 , multiply 32 two times compute the value of (23)2.

(23)2=(23)1×(23)1=32×32=94

Thus, the value of (23)2 is 94.

Expert Solution

(f)

To determine

To evaluate: The value of (16)34.

Answer

The value of (16)34 is 18.

Explanation of Solution

Consider the given expression (16)34.

Since the power is 34 , multiply 116 three fourth times compute the value of (16)34.

(16)34=(116)34=((12)4)34=(12)3=18

Thus, the value of (16)34 is 18.

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