Zero and Negative Exponents - Problem 3
Anything raised to the zero power is equal to 1. The number 2 raised to the zero power is 1, the number 100,000,000 raised to the zero power is 1. When the product of multiple bases is raised to the zero, the result is 1. You can think of it as the zero exponent is being distributed to each base in the parenthesis. Zero times any number is 0 so the new exponents for each base is 0. Anything raised to the zero is 1, now the products are essentially 1s being multiplied together, resulting in....1.
There is a couple of different ways to solve an exponent’s problem like this. One way is going to take you 3 seconds. See if you can think of that way while I do the longer way.
A lot of student when they get to these problem they remember this property, that x to the n raised to the mth power is equal to x to the n multiplied by m. Let’s try applying that here.
R to the 4th raised to the zero will be r to the 4 times zero which is like r to the zero, s to the 3 times zero is like s to the zero, then I’m going to have to t to the zero power and then I’m going to have q to the 4 times zero. q Is my base, q to the 4th times zero which is the same thing as q to the zero. What I’ve done is I’ve written it out each one of those base letters and then the products of the exponents that it’s being raised to.
Well if you remember that anything to the zero power is 1 then you could just write this as 1 times 1 times. 1 times 1 times 1 times 1 is equal to 1. That’s the answer to this kind of nasty looking problem. That’s the long way. Did you guys think of the short way?
Here’s what the short way is. If you remember that anything raised to the zero power equals 1, I wrote clouds because I like clouds, cloud to the zero power equals 1 then I know this whole thing, whatever it is raised to the zero power is one. I didn’t have to do any of this ho-ha. I could have just jumped to the right answer right from the very beginning if I remembered that anything to the zero power is equal to 1.