In this video let's cover just the basics about exponents. So an exponent looks like
this, if you have something raised to some power, �m� is called the exponent of �b�.
Now what, what does this mean when you write something this way? Well this means we're
going to take �b� and we're going to repeatedly multiply �b� by itself, again, and again,
and again, and again. And so, we don't really see anything that has a �m� in it, in
our product, but where the �m� shows up is �m� tells us how many times we're supposed
to multiply �b� times itself. So �m� times. Okay, so here's a quick example. If
you had two raised to the third power, three's your exponent, then this would be two, times
two, times two, a total of three times. And two times two, is four. Four times two, makes
eight. So two raised to third power, gives us eight. So just a quick uh, rundown of vocabulary
here. Uh, �b� is what we called the base. And in this notation the �m� is known
as the exponent. Sometimes it's called the power. Okay, so this is, these are the words
that we use. Okay, now in English here's how we say this, you probably heard me say this
on the last page. If you have a b as your base, and m as your exponent, in English we
say �b� is raised to the �mth� power. So like in this previous example, we had two
that was raised to the third power. Let's do another example, let's say we had for instance,
four raised to the second power. Then that means we're going to repeat ably multiply
four by itself, a total of two times. So four times four, is sixteen. So four raised to
the second power is called sixteen. Now two exponents in particular have special names.
This one here, if your exponent is let's say two, then we use this one so often we have
a special name for it. We say that the number is squared. So in this case we would say four
squared equals sixteen. Because your exponent specifically is two. Now if your exponent
is three, we also have a special name, this is called cubed. Now there's not special names
for every exponent under the sun, just two and three. So there, don't think that there's
a lot that you have to memorize. So four squared is sixteen. But then like here on the previous
page, two cubed is eight, because it was raised to the third power. Alright, couple other
little side things we need to mention. Exponents can be done on a calculator. Depending on
what calculator you own, it will probably be one of these two buttons here. This is
called a carrot, this is on the vast majority of calculators, especially graphing calculators.
So if you wanted to compute four squared on your calculator, then you would type four,
the carrot button, and then two, and then enter. Alright, and then when you push the
enter button, it will tell you sixteen. If you have an older style calculator, you might
have this button here where it has a �x�, and then a �y� in the exponent. And you
do it the same way. You do four exponent two, equals sixteen. Alright one last thing we
need to mention is; what happens when you have negative bases? Ah, if you have something
like negative three, let's say squared. Well this depends on whether your exponent or your
power is even or odd. If you had negative three squared, think about what this is by
definition. This is negative three times itself, which is negative three. Well wait, a negative
times a negative is actually a positive. So this will be a positive nine. So if you have
an even power, then your answer will be positive. But on the other hand, if you have an odd
power, let's take negative three cubed for example. Then by definition this is negative
three times negative three, times another negative three. But since there's an odd number
of negatives, our answer will be negative. And three times three is nine. Nine times
three, makes twenty-seven. So if you have a negative base and you have an odd power,
then your answer will be negative. So just pay attention to the sign of your answer,
depending on whether your exponent is even or odd. So anyways, I know this is a short
video and there's a lot more we can say about exponents that will be coming up later. But
at least for now, hopefully this was a good light introduction to exponents.