Step 1 :Given the expression \((-27)^{\frac{2}{3}}\), we can simplify it by taking the cube root of -27 and then squaring the result.
Step 2 :The cube root of -27 is -3, represented as \(\sqrt[3]{-27} = -3\).
Step 3 :Squaring -3 gives 9, represented as \((-3)^2 = 9\).
Step 4 :\(\boxed{9}\) is the simplified form of \((-27)^{\frac{2}{3}}\).