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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.