The exponent rule states that [tex] a^{b} × a^{c} = a^{b+c}[/tex].
[tex] \sqrt[2]{2}~*~ \sqrt[3]{2} [/tex] is equivalent to [tex]2^{\frac{1}{2} }~*~2^{\frac{1}{3} } [/tex].
You keep the coefficients the same, but add together the exponents.
[tex] \frac{1}{2}~+~\frac{1}{3}~=~\frac{3}{6}~+~\frac{2}{6}~=~\frac{5}{6} [/tex]
[tex] 2^{ \frac{5}{6}} [/tex]
OR
[tex] \sqrt[6]{2^{5}} [/tex]
OR
[tex] \sqrt[6]{32} [/tex].
