Question

Simplify cube root of 2 * fourth root od 3

Answer 1

$$\begin{gathered} \left(2^{\frac{1}{3}}\right)\times 3^{\frac{1}{4}} \\ =\left(2^{\frac{1\times 4}{3\times 4}}\right)\times 3^{\frac{1\times 3}{4\times 3}}=2^{\frac{4}{12}}\times 3^{\frac{3}{12}} \\ ={\left(2^4\right)}^{\frac{1}{12}}\times {\left(3^3\right)}^{\frac{1}{12}}={\left(2^4\times 3^3\right)}^{\frac{1}{12}}={\left(16\times 27\right)}^{\frac{1}{12}}={\left(423\right)}^{\frac{1}{12}} \end{gathered}$$