Solve this:
Q. Simplify the product :
$\sqrt[3]{2}.\sqrt[4]{2}.\sqrt[12]{32}$

Dear Student,

Please find the below required solution.

$$\begin{gathered} \sqrt[3]{2}\sqrt[4]{2}\sqrt[12]{32} = \left(2{)}^{1/3}\right(2{)}^{1/4}(32{)}^{1/12} \\ = (2{)}^{1/3}\left(2{)}^{1/4}\right(2{}^5{)}^{1/12} \\ = \left(2{)}^{1/3}\right(2{)}^{1/4}(2{)}^{5/12} \\ = (2{)}^{1/3+1/4+5/12} [ u\sin g a^m{a}^n = a^{m+n} ] \\ = (2{)}^{12/12} \\ = (2{)}^1 = 2 \end{gathered}$$

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