Nigeria

@blackwolf811 I don't believe you.

In Africa at least, Nigeria is hugely powerful and is, for my money, the most influential nation.

From a government perspective it does not get along with South Africa, the other "power" in Africa, and is not afraid to show it. It treats South Africa with disdain and dismissively showing that it has the balance of power in the relationship. The South African government seems to have no semblance of a response. Take for example the fine of MTN a South African mobile company that is the second-largest emerging markets player after Airtel. There is no doubt that MTN was in the wrong and deserved sanction but they were fined US$1,000 per subscriber when the ARPU for the offending subscribers is US$8 per month. The fine is a staggering US$5bn and is basically the value of MTN's entire mobile business in essence a f*ck off fine. Standard Bank, a South African bank that is the largest in South Africa by Assets (not profits or market capitalization) is in regulatory trouble as well under less than clear circumstances. South Africa was until 2012 the largest investor on the continent (not in Nigeria as oil-producing countries predominate Nigeria's FDI) but has now fallen to third place behind the UK and US but its investments are still significant and larger than China's for example, but Nigeria's actions are clear to South Africa: we don't want or need you and your capital here. That is power. South Africa looked as though it was in pole position to invest in the non-oil sectors of the economy Nigeria seeks to develop, especially in light of the drop in oil prices and therefore revenues but I think it is clear that South Africa is not invited and if it still wants to invest anyway (which everyone expects anyway) it will be at the pleasure and possibly even whims of the Nigerian government.

Nigeria is in the league of few nations that actively and profitably export their culture. Nollywood ranks alongside Bollywood, Holywood, British Film, and Television as regularly exported cultural products opening up new and lucrative markets for its artist particularly in South Africa. In the most recent copy of Forbes magazine, South Africa's self-proclaimed prince if hip hop, AKA, cited Nigerian artists as those who've got it right in terms of plying their trade.

Nigeria is home to the richest black man in Aliko Dangote.
Nigeria's population at circa 180m, mineral resources, arable land, and people who are very industrious who are used to less enabling environments (military dictatorships until 1999 for example) seems poised for growth too tantalizing for the world to ignore and even under great difficulty many people are sizing up and embarking on the arduous adventure of Nigerian operations where the infrastructure and various other macro enablements are underdeveloped.

In terms of power, I don't see a more powerful state on the continent.