Answer
-3
Work Step by Step
Based on the definition of $a^{\frac{m}{n}}$, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$ (where $\sqrt[n] a$ represents a real number).
Therefore, $\sqrt[4] (-3)^{4}=(-3)^{\frac{4}{4}}=(-3)^{1}=-3$.