How would you solve x^2 = 27^(2/3) WITHOUT a calculator? ?

Question

I've tried changing the right side to the cubed root of 27^2 but I couldn't solve that in my head. How would you do something like that in your head? Or is there some other way to do it?

I know that x = 3, that's not what I'm interested in. I want to know how.

Answer 1

hey ,i couldn't undersatnd ur question

is having a equal sign ( = ) i think it is needed to prove not solve

second thing how would u be able to know if am using calctr or not.

Answer 2

x^2= 27(2/3)

what you are asked to solve is this

x^2= cube root of 27 and then square that number

x^2= 27(2/3)

x^2= cube root of 27=3 and 3^2=9

x^2=9

x=3

Answer 3

x² = 27^(2/3)

take square root of both sides

(x²)^(1/2) = [27^(2/3)]^(1/2)

x = 27^(2/3 x 1/2)

x = 27^(2/6)

x = 27^(1/3)

x = (3³)^(1/3)

therefore: x = 3