To rewrite the expression \( \sqrt[3]{81} \) as a product of an integer and another irrational cube root, we first simplify \( \sqrt[3]{81} \).
First, we can express 81 as a power of 3:
\[ 81 = 3^4 \]
Now we can rewrite the cube root:
\[ \sqrt[3]{81} = \sqrt[3]{3^4} = \sqrt[3]{3^3 \cdot 3} = \sqrt[3]{3^3} \cdot \sqrt[3]{3} \]
Since \( \sqrt[3]{3^3} = 3 \), we can substitute this back in:
\[ \sqrt[3]{81} = 3 \cdot \sqrt[3]{3} \]
Therefore, the irrational cube root \( \sqrt[3]{81} \) can be rewritten as:
\[ 3 \cdot \sqrt[3]{3} \]
So the final answer is:
\[ 3 \sqrt[3]{3} \]
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