Question

If a^16 is the same as 2^64, what is the absolute value of a?

Answer 1

`a=16`

Explanation:

we know the power rule:

`(a^(m))^(n) =a^(m*n)`

In this problem we have

`a^(16)=2^(64)`

rasise both sides to 1/16

`(a^(16))^{(1)/(16)}=(2^(64))^{(1)/(16)}`

Applying the power rule

`(a)^{(16)/(16)}=(2)^{(64)/(16)`

simplify

`a=(2)^(4)`

`a=16`