"faint power" is correct and usable in written English.
It is typically used to describe something that is weak or has limited strength or influence. Example sentence: The faint power of the magnets was enough to keep the paper clip suspended in the air.
The entire constellation is enveloped in faint emission nebulosity, powered by several stars in Orion's belt rather than by the star exciting the much smaller Orion Nebula.
For years, the Drug War has been used as a pretext to lock people in prison for exorbitant lengths of time -- people whose "crimes" never hurt another human being, people who already lived at the margins of society, whose voices were the faintest and whose power was the least.
These continued detentions send an unambiguous message to those who nurture faint hopes Putin might somehow be toppled from power.
Alongside the rise of security for celebrities of even the faintest wattage, private security power has expanded in far more serious ways.
The faintest sniff of real power within the coalition has rather unbalanced that equation, and the Lib Dems have now put forward proposals for the position of MP to be considered a potential job-sharing opportunity.
C's ghostly powers are faint — he can smash the odd glass — and mostly he just trails M longingly or studies her as she, for instance, eats an entire chocolate pie (in a single four-minute take), then vomits it up.
Also in the seventies, I undertook to describe, with Mr. Shawn's faint blessing, a floating nuclear power plant that would produce twenty-three hundred megawatts of electricity and was meant to float 2.8 miles off the New Jersey coast near Atlantic City.
In 1968, huge oil reserves were discovered in Prudhoe Bay, about dead center on the coastline, and a web of pipelines, roads, power lines, and faint trails left by ground-thumping seismic survey teams has spread outward ever since.
But for a short moment I was far away, in a place where the simple dance of flames and the lonely vigil of a zebra eating tall grass in faint light still held enormous power.
He giveth power to the faint; and to them that have no might he increaseth strength.
