SOLUTION: Which of the following could be an exact value of n^4 where n is an integer? A. 1.6 x 10^20 B. 1.6 x 10^21 C. 1.6 x 10^22 D. 1.6 x 10^23 E. 1.6 x 10^24 The correct answer is

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Question 1184035: Which of the following could be an exact value of n^4 where n is an integer?
A. 1.6 x 10^20
B. 1.6 x 10^21
C. 1.6 x 10^22
D. 1.6 x 10^23
E. 1.6 x 10^24
The correct answer is suppose to be A but I don't know how.
Found 3 solutions by josgarithmetic, Theo, MathLover1:
Answer by josgarithmetic(39618)   (Show Source):
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A. 1.6 x 10^20
B. 1.6 x 10^21
C. 1.6 x 10^22
D. 1.6 x 10^23
E. 1.6 x 10^24

Basic Fact: 16=2^4

A. 16 x 10^19
B. 16 x 10^20
C. 16 x 10^21
D. 16 x 10^22
E. 16 x 10^23

Choice B, because

and the n is .

Answer by Theo(13342)   (Show Source):
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the fourth root of 1.6 * 10^20 is equal to:

(1.6 * 10^20) ^ (1/4) which is equal to:

(16 * 10^19) ^ (1/4) which is equal to:

(2 * (10^19)^1/4) which is equal to:

2 * 10^(19/4) which is not an integer.

selection 1 doesn't appear to be good.

i think it's going to be B.

B is 1.6 * 10^21.

this is equal to 16 * 10^20

the fourth root of that is (16 * 10^20) ^ (1/4) which is equal to:

16^(1/4) * (10^20)^(1/4) which is equal to:

2 * 10^5.

that's the value of n.

raise that to the 4th power to get:

(2 * 10^5) ^ 4 which gets you:

2^4 * (10^5)^4 which gets you:

16 * 10^20 which is the same as:

1.6 * 10^21.

i'd go with selection B.

Answer by MathLover1(20850)   (Show Source):
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answer is B.

then