Powers and Roots of Limits
Limits are pretty powerful. They're kind of the big idea of calculus. Throughout calculus we'll see that no matter what we're doing, there's a limit or two lurking somewhere.
The purpose of this reading isn't to totally fangirl over limits, though. Instead we'll be talking about what happens when we take a limit involving a function raised to some power. As it turns out, there's a property to help us with this very situation.
If exists, and p is any real number, then
The limit of a function that's being raised to some power is the limit of that function raised to the same power. All there is to it.
Got it? Just pull the power out of the limit.