Question
Simplify. \( \left(\sqrt[3]{x^{3} y^{2}}\right)^{12} \) \( x^{[?]} y \)
Ask by Love Powell. in the United States
Mar 11,2025
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Tutor-Verified Answer
Answer
\( x^{12} y^{8} \)
Solution
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Mind Expander
To simplify \( \left(\sqrt[3]{x^{3} y^{2}}\right)^{12} \), we first rewrite the expression inside the cube root: \[ \sqrt[3]{x^{3} y^{2}} = (x^{3} y^{2})^{1/3} = x^{3/3} y^{2/3} = x^{1} y^{2/3} \] Now, raise this entire expression to the 12th power: \[ \left(x^{1} y^{2/3}\right)^{12} = x^{1 \cdot 12} y^{(2/3) \cdot 12} = x^{12} y^{8} \] So, the simplified form is \( x^{12} y^{8} \). Hence, in the format requested: \( x^{[12]} y^{8} \)
