12 over 512^1/6?

Question

How do I solve this without* a calculator? i.e., with a pencil and paper.

Answer 1

If you know that 512 is 2^9, it falls out rather easily.

(If you don't get 3 times the square root of 2, you did it wrong.)

Answer 2

For, 12/ (512^(1/6)), you have to factorize the numerator and denominator in terms of 2,
= (2^2)(3) / ((2^9)^1/6))
= (2^2)(3) / (2^(9/6))
= (2^2)(3) / (2^(3/2))
Taking common factors of 2,
= (2^(2-3/2) (3)
= (2^(1/2)) (3)
= sqrt(2)*(3)

where sqrt = the square root sign

Answer 3

12 / 512^1/6

I think you must be clear that 2^9 = 512
and 12 = 3 X 4 = 3 X 2^2

Now 3 X 2^2 / 2^9

= 3/ 2^7 OR

= 3 X 2^(-7)

Answer 4

512 ^ 1/6 is the same as
the 6th root of 512 which is the
6th root of 8*64....
the 6th root of 64 is 2,
so you get the denominator as
2(6th rt of 8)...
the top is 12, so
12/2 reduces to 6/1
so the final is
6/ 6th root of 8
hope you understand!

Answer 5

12/512^1/6
=12/(sixthroot of 512)

root of 512 is 2^9; take six of them out leaving 2(sixthroot(8))

12/(2(sixthroot(8)) = 6/(sixthrooth(8))

multiply by denominator to get 6(sixthroot(8))/2
reducing to 3 * (sixthroot(8))