To rewrite the expression \( \sqrt[3]{81} \) as a product of an integer and another cube root, we first simplify the term:
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We know that \( 81 = 3^4 \). Therefore, \[ \sqrt[3]{81} = \sqrt[3]{3^4}. \]
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We can break this down into two parts. Using the property of cube roots, we write: \[ \sqrt[3]{3^4} = \sqrt[3]{3^3 \cdot 3^1} = \sqrt[3]{3^3} \cdot \sqrt[3]{3^1}. \]
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We know that \( \sqrt[3]{3^3} = 3 \). So, we have: \[ \sqrt[3]{3^4} = 3 \cdot \sqrt[3]{3}. \]
Thus, the expression \( \sqrt[3]{81} \) can be rewritten as: \[ 3 \cdot \sqrt[3]{3}. \]
So, the final answer is: \[ 3 \sqrt[3]{3}. \]
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