[CMB]Some questions about power spectrum

["pihou"]

I've started CMB study recently. Power spectrum is very important
concept, but why we usually use k^3P(k) instead of P to represent the
power spectrum? And how does the power-law come from? Especially, why
is the scale-invariant spectrum(Harrison-Zel'dovich spectrum) so
important and useful?
Any suggestions? Some books or papers should I read to resolve my
problems?
Thanks.