#3**+1 **

Let's take term by term

8^(2/3) means (8^2)^(1/3) = 64^(1/3) = cube root of 64 = 4 this term will be outside the final radical

(x^7)^(2/3) = x^(14/3) = x^(4 + 2/3) ......x^4 will be outside the final radical......x^2 will be inside the final radical

(y^4)^(2/3) = x^(8/3) = y^(2 + 2/3) .....y^2 will be outside the final radical....y^2 will be inside the final radical

The index of the radical will be the denominator of each of the fractions above ....i.e., 3

So.....the final answer is

4x^2y^2 ∛ [ x^2 * y^2 ]

CPhill Jan 10, 2019