Posted by Liz on .
Simplify  2/(the 6th root of 81)

Algebra II 
MathGuru,
Let's break this down:
The sixth root of 81 = 81^(1/6)
81 is 9^2, so we have 9^(2*1/6) = 9^(1/3) or the cubed root of 9.
Therefore, to get rid of the radical in the denominator, multiply by the equivalent of 1. Multiply by the cubed root of 3 divided by the cubed root of 3.
2/(cubed root of 9) * (cubed root of 3)/(cubed root of 3)
Now we have:
2(cubed root of 3)

(cubed root of 9)(cubed root of 3)
2(cubed root of 3)

(cubed root of 27)
Finally:
2(cubed root of 3)

3
I hope this helps.