(( cube square root of 7)^1/2)^3

no idea what a cube square root is, but if you mean cube root, than

((∛7)^1/2)^3

Since (∛7)^3 = 7, we have

7^1/2 = √7

In other words,

(7^1/3)^1/2 ^3 = 7^(1/3 * 1/2 * 3) = 7^1/2