((^3√x)^4)^2 = x 8/3

To simplify the expression ((^3√x)^4)^2, we can apply the exponent rules. First, let's simplify (^3√x)^4:

(^3√x)^4 = (x^(1/3))^4

Using the exponent rule for raising a power to a power, we multiply the exponents:

(x^(1/3))^4 = x^((1/3)*4)

x^((1/3)*4) = x^(4/3)

Now, let's simplify (x^(4/3))^2:

(x^(4/3))^2 = x^((4/3)*2)

x^((4/3)*2) = x^(8/3)

Therefore, ((^3√x)^4)^2 simplifies to x^(8/3).