Sample Solution from
Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112280
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 expression (−3)4 without using a calculator.

Answer

The value of the expression (−3)4 is 81_.

Explanation of Solution

Given expression is (−3)4.

Obtain the value as follows.

(−3)4=(−3)×(−3)×(−3)×(−3)=9×9=81

Therefore, the value of the expression (−3)4 is 81_.

Expert Solution

(b)

To determine

To evaluate: The expression −34 without using a calculator.

Answer

The value of the expression −34 is −81_.

Explanation of Solution

Given expression is −34.

Obtain the value as follows.

−34=−(3×3×3×3)=−(9×9)=−81

Therefore, the value of the expression −34 is −81_.

Expert Solution

(c)

To determine

To evaluate: The expression 3−4 without using a calculator.

Answer

The value of the expression 3−4 is 181_.

Explanation of Solution

Given expression is 3−4.

Obtain the value as follows.

3−4=134=13×3×3×3=19×9=181

Therefore, the value of the expression 3−4 is 181_.

Expert Solution

(d)

To determine

To evaluate: The expression 523521 without using a calculator.

Answer

The value of the expression 523521 is 25_.

Explanation of Solution

Given expression is 523521.

Obtain the value as follows.

523521=523−21                   (∵   aman=am−n)=52=5×5=25

Therefore, the value of the expression 523521 is 25_.

Expert Solution

(e)

To determine

To evaluate: The expression (23)−2 without using a calculator.

Answer

The value of the expression (23)−2 is 94_.

Explanation of Solution

Given expression is (23)−2.

Obtain the value as follows.

(23)−2=1(23)2=1(2232)=1(49)=94

Therefore, the value of the expression (23)−2 is 94_.

Expert Solution

(f)

To determine

To evaluate: The expression 16−34 without using a calculator.

Answer

The value of the expression 16−34 is 18_.

Explanation of Solution

Given expression is 16−34.

Obtain the value as follows.

16−34=(1614)−3=(164)−3=(2)−3=18

Therefore, the value of the expression 16−34 is 18_.

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