5 over (1024^1/6)?

Question

The answer is (5 times 2^1/3) / 4; how do I arrive at it?

Answer 1

1024 = 2^10,

So, 1024^1/6 = 2^10^1/6 = 2^10/6 = 2^5/3

Finally, 5 / 2^5/3 = 5 * 2^1/3 / 2^5/3 * 2^1/3 = 5 * 2^1/3 / 2^2 = 5 * 2^1/3 / 4

Answer 2

You must know 1024 = 2 ^10

1024 ^1/6 = 2^ ( 10x1/6)
= 2^ 10/6

= 2^ 5/3

Now 5 over (1024^1/6)

= 5 over 2^ 5/3

= 5 X 2 ^( -5/3)

Beacause 2^(-5/3) = 1 over 2^(5/3)

Multiply this one by 4 and divide by 4 = 2^2

= 5 X 2 ^(-5/3 + 2) / 2^2

= 5 X 2^1/3 / 2^2

= { 5 X 2^1/3 }/4

Answer 3

10240