To solve the equation, we need to eliminate the rational exponent. We can do this by raising both sides of the equation to the reciprocal of the exponent.
x^(2/3) = 64^(1/3)
Raising both sides to the reciprocal of 2/3 (which is 3/2), we get:
(x^(2/3))^(3/2) = (64^(1/3))^(3/2)
Simplifying, we have:
x^(2/3 * 3/2) = 64^(1/3 * 3/2)
x^(1) = 64^(1/2)
x = 64^(1/2)
Taking the square root of 64, we have:
x = √64
x = 8
So, the solution to the equation x^(2/3) = 64 is x = 8.