I am having problems understanding how to multiply radicals i.e (($√5 )(^3√2)$). I know the answer is $ ^6√500 $. I just do not understand how to get there.
Update: I've solidified my understanding of this question but my current methodology leads me to -> (125^(3/6))(4^(2/6)). Which leads me to the answer -> $ ^6√500^5 $.
What am i doing wrong to lead me to this answer with the extra exponent of $ ^5 $
Since $\sqrt{5} = 5^{1/2} = (5^3)^{1/6}$ and $\sqrt[3]{2} = 2^{1/3} = (2^2)^{1/6}$, we get $\sqrt{5}\sqrt[3]{2} = (5^3)^{1/6}(2^2)^{1/6} = 500^{1/6} = \sqrt[6]{500}$.