Pre algebra problem we are stuck on

[Patricia]

The problem we are stuck on is as follows. It asks us to explain why
2^-3 is equal to 1/2^3. In looking at it we feel the answer should be
1/8. Could you give us your thoughts on this

 

[daon]

You are correct, but so is the book. 2^-3 = 2^(3)(-1) = (2³)^-1 = (8)^-1 = $\displaystyle \frac{1}{8}$ = $\displaystyle \frac{1}{2^3}$.

See how they are the same thing?