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# Evaluating exponential expressions 2

Evaluating exponential expressions 2. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Evaluate the expression 4n
to the first power minus 2n to the zeroth power for n
equals 1 and n equals 5. So, let's do n equals 1 first. So, every place we see an
n, let's put a 1 in there. So this is equal to 4 times 1 to
the first power minus 2 times 1 to the zeroth power. Every place we saw an
n, we have an n there. We have an n to the
first, one to the first. So remember, we want to do
our order of operations. We have PEMDAS. And I'm going to write it
this way just to make it clear that we do parentheses
then exponentiation. Then multiplication and
division are at the same level, they get the same priority. And then addition
and subtraction get the same priority. So, we want to do our exponents
before we do anything else. There are no parentheses here. So, we first want to evaluate
one to the first power. And anything to the first
power is just that anything. If I just have any number
to the first power, that is just going to
be equal to that number. So, 1 to the first power
is just equal to 1. So, this is going
to be 4 times 1. Let me write it. 4 times 1 minus 2 times
1 to the zeroth power. Now, any number other
than 0 to the zeroth power is going to be 1. So, if I tell you x to the
zeroth power is equal to what? And I tell you that
x is not equal to 0. What is x to the zeroth power? You should immediately
know that it is equal to 1. I exclude 0 because
0 to the zeroth power is usually undefined. Or for our purposes, you can
accept it to be undefined. And maybe in the
future, I'll do a video on explaining why
it's undefined. There's some good arguments
for why this should be 0. Because 0 to pretty much
any other power is a 0. But then there's a
really good argument for why it should be 1. Because any other number
to the zeroth power is 1. So that's why,
for the most part, we like to keep this undefined. So with that said, 1
to the zeroth power is just going to be 1. Anything other than 0 to
the zeroth power is 1. So, we have 4 times 1, which is
4, minus 2 times 1, which is 2. So, 4 minus 2 is
just equal to 2. Now, let's do the same
thing with n equals 5. So it becomes 4 times 5 to the
first power minus 2 times 5 to the zeroth power. Same thing. 5 to the first power is
just going to be equal to 5. So, I want to do that
in a different color. 5 to the first power is
just going to be equal to 5. 5 to the zeroth power is
just going to be equal to 1. And so, this expression becomes
4 times 5 minus 2 times 1. Or 4 times 5 is 20, minus
2 times 1, that is 2. And this is equal to 18. And we're done.