Hi im lost on my last question.

Question

k^-3 = 1/256

this is negative exponets "^-3" that is a negative exponent, I need to know the value of k?

a)-64
b)-4
c)4
d)64

I was thinking 64, eh I don't understand this one. Thanks!

Answer 1

k^-3 = 1/k^3

So, you want

1/k^3 = 1/256
k^3 = 256

Now, 256 = 2^8, so

k = 2^(8/3) = 2^2 * 2^(2/3) = 4∛4

Hmmm. we got trouble.
(a) and (b) are out.

4^-3 = 1/4^3 = 1/64
64^-3 = 1/64^3 = 1/4096

I think that 1/256 is a mistake.
Or, the -3 is a mistake.

16^-2 = 1/16^2 = 1/256

The whole thing is a mess.