To find the cube root of 81, we can express it as:
\[ \sqrt[3]{81} \]
The number 81 can be rewritten as \(3^4\) since \(81 = 3 \times 3 \times 3 \times 3\).
Now we can proceed to find the cube root:
\[ \sqrt[3]{81} = \sqrt[3]{3^4} = 3^{4/3} = 3^{1 + 1/3} = 3^1 \cdot 3^{1/3} = 3 \cdot \sqrt[3]{3} \]
Thus, the cube root of 81 is:
\[ 3 \sqrt[3]{3} \]
So, \(\sqrt[3]{81} = 3 \sqrt[3]{3}\).