urgent help, proving something?

Alright I'm working on trying to prove something from Spivak's calc book, but I don't even know where to start. I'll post the problem, and then my thoughts on it. I've been trying really hard, but I'm struggling.

Quote:

6a. Prove that if 0 is less than or equal to x which is less than y, then x^n < y^n, n = 1, 2, 3...

b. Prove that if x < y and n is odd, then x^n < y ^n.

c. Prove that if x^n = y^n and n is odd, then x = y.

d. Prove that if x^n = y^n and n is even, then x = y or x = -y.

Okay so I think I may have a start but I'm having trouble. I know *why*, for instance, c and d are true, but I don't know how to prove it.

6a. I'm not sure how I would do this but my start: x^n < y^n. N = 1, so x < y. If n is two, you can start with x < y. Then you square both sides to get x^n < y^n. Etc. How do I prove this for all n?

okay so my problem with every one of these is that I don't know how to prove this for n. I can do this I think for specific numbers, but I have no idea for n. Can someone please provide me with some assistance? I'm supposed to hand in a problem explaining this tomorrow.