To find the cube root of 81, we can express it as:
\[ 81^{1/3} \]
Since \(81\) can be expressed as \(3^4\) (because \(3^4 = 81\)), we can rewrite the cube root as:
\[ (3^4)^{1/3} = 3^{4/3} = 3^{1 + 1/3} = 3^1 \cdot 3^{1/3} = 3 \cdot \sqrt[3]{3} \]
Thus, the cube root of \(81\) does not simplify to a whole number. The approximate decimal value of \(81^{1/3}\) is about \(4.326\).
None of the provided responses (9, \(81^{1/3}\), -9, 27) are correct since \(81^{1/3}\) is not a whole number.
However, if you're looking for the expression for the cube root of 81, the correct answer would be:
\(81^{1/3}\).