Question

If $n^k=64$ and $n$ and $k$ are integers, which of the following cannot be a value of $n$?

• A. $16$
• B. $8$
• C. $4$
• D. $2$
• E. $-2$

Answer 1

The correct option is A $16$

Factors of $64$ are: $2\times 2\times 2\times 2\times 2\times 2=2^6$

$\therefore 64=2^{6}or{4}^{3}or{8}^{2}or{64}^{1}or{(-2)}^{6}or{(-8)}^2$

Comparing all these with $n^k$

$n$ can be $-8,-2,2,4,8,64$

and

$k$ can be $1,2,3,6$