To simplify \( \sqrt[3]{54} \), we can start by breaking down the number 54 into its prime factors.
The prime factorization of 54 is:
\[ 54 = 2 \times 3^3 \]
Now, we can use this factorization to simplify the cube root:
\[ \sqrt[3]{54} = \sqrt[3]{2 \times 3^3} \]
Using the property of cube roots, we can separate this as follows:
\[ \sqrt[3]{54} = \sqrt[3]{2} \times \sqrt[3]{3^3} \]
Since \( \sqrt[3]{3^3} = 3 \), we can simplify further:
\[ \sqrt[3]{54} = \sqrt[3]{2} \times 3 \]
Thus, the simplified form of \( \sqrt[3]{54} \) is:
\[ 3 \sqrt[3]{2} \]
So, the final answer is:
\[ \sqrt[3]{54} = 3\sqrt[3]{2} \]