Simplify - 2/(the 6th root of 81)
To simplify this expression, we need to evaluate the sixth root of 81 and then divide 2 by that value.
Step 1: Find the sixth root of 81.
The sixth root of a number can be found by raising that number to the power of (1/6). In this case, we need to find the sixth root of 81.
The sixth root of 81 = 81^(1/6).
Step 2: Evaluate the sixth root of 81.
Using a calculator or a mathematical software, we can find that the sixth root of 81 is approximately 2.618.
Therefore, 81^(1/6) ≈ 2.618.
Step 3: Divide 2 by the result from Step 2.
Now, we divide 2 by the value we obtained in Step 2.
2 / 2.618 ≈ 0.764.
So, simplifying -2/(the 6th root of 81) gives us approximately -0.764.
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.