To simplify the expression \( \sqrt[3]{54} \), we can factor 54 into its prime factors.
First, factor 54: \[ 54 = 2 \times 27 = 2 \times 3^3 \]
Now, we can rewrite \( \sqrt[3]{54} \): \[ \sqrt[3]{54} = \sqrt[3]{2 \times 3^3} \]
Using the property 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: \[ \sqrt[3]{54} = \sqrt[3]{2} \times 3 \]
Thus, the simplified form of \( \sqrt[3]{54} \) is: \[ 3 \sqrt[3]{2} \]
So, \( \sqrt[3]{54} = 3 \sqrt[3]{2} \).