# How do you write root5 (96s^14t^20) in simplified radical form?

Mar 24, 2017

First factor everything, keeping in mind that we're looking for things to the fifth power.

$\sqrt[5]{96 {s}^{14} {t}^{20}} = \sqrt[5]{{2}^{5} 3 {s}^{5} {s}^{5} {s}^{4} {t}^{5} {t}^{5} {t}^{5} {t}^{5}}$

Now take out the fifth root of fifth powers

$\sqrt[5]{{2}^{5} 3 {s}^{5} {s}^{5} {s}^{4} {t}^{5} {t}^{5} {t}^{5} {t}^{5}} = 2 \cdot s \cdot s \cdot t \cdot t \cdot t \cdot t \cdot \sqrt[5]{3 {s}^{4}} = 2 {s}^{2} {t}^{4} \sqrt[5]{3 {s}^{4}}$

Always check the Even-Even-Odd rule:
If the index of the radical is even and the exponent of the original variable is even and the exponent of the final variable is odd, you need absolute value bars. In this case it's not necessary because the index of the radical is 5, which is odd, but you can learn more about the rule below.
http://planetmath.org/evenevenoddrule