This ? concerns math (intermediate alg.). Could someone tell me if I'm doing this right, please?

Question

This ? concerns roots. Here is the problem:

8 5/6 (this problem follows the rule of: a m/n = n, then the "square root" sign; then, inside the sq. root, a to the m power)

8 5/6= 6th root of 8 to the 5th power

So, it is the 6th root of 32, 768.

I don't have a calculator w/ me, so
I couldn't give you the answer.

Anyway, I believe that 6th root of 8 to
the 5th power is the answer (short of
solving that final part of the problem).

Answer 1

You could convert 8 to 2^3 and then it becomes (2^3)^(5/6) and since powers to powers multiply, you now have

2^(5/2) = 2^(2 and 1/2) = 2^2 * 2^(1/2) = 4 sqrt 2

Answer 2

seems the carat (^) is used with the exponent term in Yahoo!Answers
so 8^(5/6)
now, 8 = 2^3, so 8^(5/6) = 2^[3*(5/6)]=2^(5/2)
roots are the "evolution" of a number, which means it gets smaller in value
powers are the "involution" of a number, which means the number gets bigger
so 8^(5/6) = sqrt(32) = 4 sqrt(2)
all without a calculator

Answer 3

You're doing it fine and your answer is right.
Let's finish it: Note that 8^5 = 2^15 = 32768
We want 32768 ^1/6 = 2^(15/6) = 2^(5/2) = 32^(1/2)
= √32 = 4√2 = 5.656(approx).