Rules of Exponents-Exponents of 0 and 1

[One speaker] 

Narrator: Hi, welcome to the video on rules of exponents for the exponents 0 and 1.  So any base, like a,  raised to the power of 1, is just equal to itself, a. Or a multiplied to itself just one time, which equals a. [] that’s pretty obvious. We can also see it in the form of , that would also equal . And this,[]   is the same as  which is equal to a four times in the numerator and a three times in the denominator [] Then we can cancel three of the a’s in both the numerator and the denominator, leaving us with just one a in the numerator which is the same as  or in other words, just a. So is just itself, just a. It makes sense, anything raised to the one power is just itself. But what is ? This one’s a little bit harder to think about. How do we come up with this? Wel,, we can figure out an exponent of zero just by taking something like .  So we can come up with an example of something raised to the zero power. But now, let’s figure out what this means. Well, if we use this example of   this is also equal to a multiplied twice in the numerator and a multiplied twice in the denominator.  If that’s the case, then we can cancel two a’s from both the numerator and the denominator and we’re just left with one times one which equals one. So a to the zero power is equal to one.  This is true for any a, but actually, there’s one circumstance where it’s not true. If a is zero, .  This is just undefined. Zero to the zero power in the only exception for this rule. So a cannot be equal to zero. Let’s use a number, .  Let’s think of a way that we can have a zero power exponent. It could be a scenario such that .  This is the same as . If we expand this to help us see how we simplify it, it looks something like  . Once again, each of these can divide each other out. It just becomes one times one times one times one, which equals one. So  is also equal to one. And that’s true for any number, ,  , anything raised to the zero power is one.

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