(cube root)2 * (4 root)2 * (12 root )32

Dear Student,

Please find below the solution to the asked query:

We have : $\sqrt[3 ]{2} \times \sqrt[4 ]{2} \times \sqrt[12 ]{32}$ , So

$$\begin{gathered} \Rightarrow \sqrt[3 ]{2} \times \sqrt[4 ]{2} \times \sqrt[12 ]{2\times 2\times 2\times 2\times 2} \\ \Rightarrow \sqrt[3 ]{2} \times \sqrt[4 ]{2} \times \sqrt[12 ]{2^5} \\ \Rightarrow 2^{\frac{1}{3}} \times 2^{\frac{1}{4}} \times {\left( 2^5\right)}^{\frac{1}{12}} \\ \Rightarrow 2^{\frac{1}{3}} \times 2^{\frac{1}{4}} \times 2^{\frac{5}{12}} ( \mathrm{We} \mathrm{know} {\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}} = {\mathrm{a}}^{\mathrm{m}\times \mathrm{n}} ) \\ \Rightarrow 2^{\frac{1}{3}+\frac{1}{4}+\frac{5}{12}} ( \mathrm{We} \mathrm{know} {\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}} = {\mathrm{a}}^{\mathrm{m}+\mathrm{n}} ) \\ \Rightarrow 2^{\frac{4 \hspace{0.17em}+ 3 + 5}{12}} \\ \Rightarrow 2^{\frac{12}{12}} \\ \mathbf{\Rightarrow }\mathbf{ }\mathbf{2}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards