What is the meaning of 64^(2/3)

64^2/3 = (64^1/3)², or (³√64)²

So..what times itself 3 times equals 64?

4*4*4 = 64.

(³√64)²

(4)²

16 is our answer.

Does this make sence?

It means that we are raising 64 to the 2/3rds power (exponent).

By a property of exponents, we can write this as (64^1/3)².   And 64^1/3 means the same thing as ³√64 which is the "cube root" of 64 which = 4.

So, we have  (4)²  = 16

And there's your answer  !!!

If x = 64^2/3 then x³ = 64² so x is a number which, when cubed is the same as 64 squared.  That is, 64^2/3 is a number which when cubed is the same as 64².

$${{\mathtt{16}}}^{{\mathtt{3}}} = {\mathtt{4\,096}}$$

$${{\mathtt{64}}}^{{\mathtt{2}}} = {\mathtt{4\,096}}$$

So 16 is 64^2/3 because 16³ is the same as 64².

Thank you everyone. That helped a lot!