Solve the expression: $12\sqrt[4]{15} \ \div \ 8\sqrt[3]{3}$

Given: $12\sqrt[4]{15} \ \div \ 8\sqrt[3]{3}$
 

To do: Solve the expression

Solution: $12\sqrt[4]{15} \ \div \ 8\sqrt[3]{3}$

=$\frac{\frac{}{} 12\sqrt[4]{15} \ }{\ 8\sqrt[3]{3}}$

=$\frac{3\times ( 3\times 5)^{\frac{1}{4}}}{2( 3)^{\frac{1}{3}}}$

=$\frac{3\times 3^{\frac{1}{4}} \times 5^{\frac{1}{4}}}{2( 3)^{\frac{1}{3}}}$

=$\frac{{3^{1+\frac{1}{4} -\frac{1}{3}}} \times 5^{\frac{1}{4}}}{2}$

=$\frac{3^{\frac{11}{12}} \times 5^{\frac{1}{4}}}{2}$

Therefore the solution of the equation is =$\frac{3^{\frac{11}{12}} \times 5^{\frac{1}{4}}}{2}$

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Updated on: 10-Oct-2022

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