How do you simplify  ""^5sqrt(96)

Oct 25, 2014

$\sqrt[5]{96}$

$\implies \sqrt[5]{{2}^{5} \cdot 3}$

$\implies \sqrt[5]{{2}^{5}} \cdot \sqrt[5]{3}$

$\implies 2 \sqrt[5]{3}$

Oct 25, 2014

Since $96 = {2}^{5} \cdot 3$,

$\sqrt[5]{96} = \sqrt[5]{{2}^{5} \cdot 3}$

by distributing the 5th-root,

$= \sqrt[5]{{2}^{5}} \cdot \sqrt[5]{3}$

by cancelling out the 5th-power and the 5th-root,

$= 2 \sqrt[5]{3}$.

I hope that this was helpful.