X^-2/3 = 64/9, what is x?

Note that....... a^-b = 1/a^b

So (x)^-2/3  = 1/x^2/3

So we have  

1/x^2/3    =  64/9           Note something, that if two fractions are equal, then so are their reciprocals.....so we have

x^2/3  =  9/64               Now, to get x by itself, raise each side to the 3/2 power....so we have

(x^2/3 )^3/2 =  (9/64)^3/2 

x = (9/64)^3/2               Note that the expression on the right can be written as [(9/64)^1/2 ]³ which is the same thing as  [√(9/64)]³  = (3/8)³  = 3³/ 8³   = 27 / 512

And that's our answer....