Answer
See below for proof that the Power Rule holds for the function $x^{3/4}$.
Work Step by Step
$$x^{3/4}=\sqrt{x\sqrt x}=(x\times x^{1/2})^{1/2}=(x^{3/2})^{1/2}$$
Using the Chain Rule, we have $$\frac{d}{dx}(x^{3/2})^{1/2}=\frac{1}{2}(x^{3/2})^{-1/2}(x^{3/2})'=\frac{1}{2}(x^{3/2})^{-1/2}\times\frac{3}{2}x^{1/2}$$
$$=\frac{3}{4}x^{-3/4}\times x^{1/2}=\frac{3}{4}x^{-1/4}=\frac{3}{4}x^{3/4-1}$$
So the Power Rule $(x^n)'=nx^{n-1}$ holds for the function $x^{3/4}$.