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Divide 12 x 4th root of 15 by 8 x cube root 3

Dear Student

we have

\frac{12 \sqrt[4]{15}}{8 \sqrt[3]{3}} = \frac{3 (15)^{\frac{1}{4}}}{2 (3)^{\frac{1}{3}}} = \frac{3 3^{\frac{1}{4}} 5^{\frac{1}{4}}}{2 3^{\frac{1}{3}}} \Rightarrow \frac{3^{1 + \frac{1}{4} - \frac{1}{3}} . 5^{\frac{1}{4}}}{2} = \frac{3^{\frac{12 + 3 - 4}{12}} 5^{\frac{1}{4}}}{2} \Rightarrow \frac{3^{\frac{11}{12}} 5^{\frac{1}{5}}}{2}

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