QuestionJuly 14, 2025

Use the distributive property to help simplify the expression. 3sqrt [3](3)+5sqrt [3](81)-3sqrt [3](24) 14sqrt [3](3) -12sqrt [3](3) 12sqrt [3](3) -12sqrt [3](2)

Use the distributive property to help simplify the expression. 3sqrt [3](3)+5sqrt [3](81)-3sqrt [3](24) 14sqrt [3](3) -12sqrt [3](3) 12sqrt [3](3) -12sqrt [3](2)
Use the distributive property to help simplify the expression.
3sqrt [3](3)+5sqrt [3](81)-3sqrt [3](24)
14sqrt [3](3)
-12sqrt [3](3)
12sqrt [3](3)
-12sqrt [3](2)

Solution
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Answer

12\sqrt[3]{3} Explanation 1. Simplify each term 5\sqrt[3]{81} = 5\sqrt[3]{3^4} = 5 \cdot 3\sqrt[3]{3} = 15\sqrt[3]{3} -3\sqrt[3]{24} = -3\sqrt[3]{2^3 \cdot 3} = -3 \cdot 2\sqrt[3]{3} = -6\sqrt[3]{3} 2. Combine like terms 3\sqrt[3]{3} + 15\sqrt[3]{3} - 6\sqrt[3]{3} = (3 + 15 - 6)\sqrt[3]{3} = 12\sqrt[3]{3}

Explanation

1. Simplify each term<br /> $5\sqrt[3]{81} = 5\sqrt[3]{3^4} = 5 \cdot 3\sqrt[3]{3} = 15\sqrt[3]{3}$<br /><br /> $-3\sqrt[3]{24} = -3\sqrt[3]{2^3 \cdot 3} = -3 \cdot 2\sqrt[3]{3} = -6\sqrt[3]{3}$<br /><br />2. Combine like terms<br /> $3\sqrt[3]{3} + 15\sqrt[3]{3} - 6\sqrt[3]{3} = (3 + 15 - 6)\sqrt[3]{3} = 12\sqrt[3]{3}$
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