Absolutely. I think this is a major factor for the gender pay gap. Women on average do not negotiate.

I have negotiated and I have ended up being paid more than male colleagues simply because I asked for it and I also had experience and proof for why I was worth it.

Negotiation is a major life skill! If you are good at your job, you have power. I have even gotten offers from recruiters that I took back to my current job and said "hey this is what this headhunter wants to pay me, can you match it so I can stay" and ended up with all sorts of awesome perks and pay rises.