"extend their power" is correct and usable in written English.
This phrase can be used in many contexts, such as to refer to people trying to increase their influence or control over something. For example, "The government sought to extend their power to the remote villages in the region."
Many of America's rivals used America's travails in Iraq to extend their power: Iran is more powerful than it was in 2000, and closer to acquiring a nuclear bomb; Russia and China have extended their web of alliances and strengthened their regional influence.
But they in turn find it difficult to extend their power across tribal lines.
His successors would extend their power over the whole of China, Persia, and most of Russia.
Those seeking information, as George Orwell warned, do so to extend their power.
He said: "It's only fair if you approve of the policies of a government, if you want to extend their power, why not do it?
Rebating was a common pricing tactic during the 19th century and was often used by large industrialists to preserve or extend their power by undercutting competition.
Yet, many of the people working in tech see the US and UK police and intelligence agencies and wonder why they're so keen to extend their powers.
Jagdish Bhagwati, an economics professor at Columbia University, wants developing countries everywhere to extend their powers to tax their expatriates, in order to reclaim some of the value created abroad by highly skilled emigrants.
LONDON — Some of the world's most powerful central bankers and financial regulators are proposing that the Securities and Exchange Commission and its counterparts in other countries extend their powers to include the regulation of executive compensation.
It creates expensive government bureaucracies that seize on any excuse rules relating to inter-state commerce are a particular favourite to extend their powers to boss people about or spy on them.
"Our anxiety is that there are some people in the UK government who appear to believe that without the European Union somehow those powers are floating free and they will hang onto them and then say they'll hand them to us - they already lie with us". Welsh Secretary Alun Cairns said the Repeal Bill would offer devolved administrations the opportunity to extend their powers.
