Question

How do you write `1/(3sqrt2^-n)` as a fractional exponent?

Answer 1

`color(red)(1/(3(sqrt2)^(-n)) = 2^(n/2)/3)`

Explanation:

`1/x^(-n)= x^n`, so

`1/(3(sqrt2)^(-n)) = (sqrt2)^n/3 = (2^(1/2))^n/3`

Also, `(x^a)^b = x^(ab)`, so

`(2^(1/2))^n/3 = 2^(n/2)/3`

∴ `1/(3(sqrt2)^(-n)) = 2^(n/2)/3`