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If a^(b/4)=16 for positive integers a an...

If `a^(b/4)=16` for positive integers a and b, what is one possible value of b ?

A

3

B

1/2

C

4

D

20

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Number 16 can be written in exponential form `a^(b/4)`, where a and b are positive intergers as follows : `2^4 , 4^2 , 16^1 , (16^2)^(1/2) , (6^4)^(1/4)` . Hence , if `a^(b/4)=16` , where a and b are positive integers , then `b/4` can be `4,2,1,1/2` , or `1/4`. So the value of b can be 16, 8, 4, 2, or 1. Any of these values may be gridded as the correct answer.
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