Evaluate each expression without using a calculator.
- (a) (−3)4
- (b) −34
- (c) 3−4
- (d) 523521
- (e) (23)−2
- (f) 16−3/4
(a)
To evaluate: The expression (−3)4 without using a calculator.
Answer to Problem 1ADT
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_.
(b)
To evaluate: The expression −34 without using a calculator.
Answer to Problem 1ADT
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_.
(c)
To evaluate: The expression 3−4 without using a calculator.
Answer to Problem 1ADT
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_.
(d)
To evaluate: The expression 523521 without using a calculator.
Answer to Problem 1ADT
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_.
(e)
To evaluate: The expression (23)−2 without using a calculator.
Answer to Problem 1ADT
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_.
(f)
To evaluate: The expression 16−34 without using a calculator.
Answer to Problem 1ADT
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=(4√16)−3=(2)−3=18
Therefore, the value of the expression 16−34 is 18_.
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Chapter T Solutions
Essential Calculus: Early Transcendentals
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