To simplify the cube root of 54, we can start by factoring 54 into its prime factors:
\[ 54 = 2 \times 3^3 \]
Now, we can express \(\sqrt[3]{54}\) using its prime factors:
\[ \sqrt[3]{54} = \sqrt[3]{2 \times 3^3} \]
Using properties of cube roots, we can separate the factors:
\[ \sqrt[3]{54} = \sqrt[3]{2} \times \sqrt[3]{3^3} \]
Since \(\sqrt[3]{3^3} = 3\), we have:
\[ \sqrt[3]{54} = 3 \times \sqrt[3]{2} \]
Thus, the simplified form of the cube root of 54 is:
\[ \sqrt[3]{54} = 3\sqrt[3]{2} \]