Simplify - 2/(the 6th root of 81)

Answer 1

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)
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3

I hope this helps.