Exponent Rules 1 - Algebra, Mathematics Video Lecture

We're asked to simplify
9 squared.
And that quantity, whatever 9
squared is, we know what it
is, it's 81, but we'll
keep it at 9 squared.
They need to simplify 9 squared
to the third power.
And they want us to express
our answer in exponential
form, which is just another way
of saying that they want
us to keep it as exponents.
They don't want us to multiply
it out and get some really
really large number.
So think about how to do this.
So we have 9 squared
to the third power.
Well the simplest way to do this
is just if you know the
exponent rule, or the exponent
property, that if you raise
something to an exponent, and
then if you raise that entire
thing to another exponent, then
you can just multiply
these two exponents.
So this is going to be the same
thing as 9 to the 2 times
3 power, which is the same thing
as 9 to the sixth power.
And we'd be done.
We've expressed our answer in
exponential form, 9 to the
sixth power, we've simplified.
Now you say, what's not
exponential form?
What's not exponential form is
if we would actually multiply
9 times 9 times 9 times 9 times
9 times 9, which is
going to be a very very
large number.
And we'd probably want a
calculator or it would
take us some time.
So 9 to the sixth
is the answer.
Now another way to view it, if
you don't like that formula,
is we could even apply
other formulas.
What's another way to think
about 9 squared
to the third power?
I'll do this in a different
color just for fun.
9 squared times 9 squared
times 9 squared.
This is 9 squared to
the third power.
And we also know the other
exponent property, or the
other exponent rule.
That if you have the same base
being raised to different
powers, in this case
they're all being
raised to the same power.
And you're taking the product of
them, then this is the same
thing as taking that same base,
that 9, and raising it
to the sum of the powers.
So 9 to the 2 plus 2 plus
2, which is once
again, 9 to the 6.
I don't even have to
write it again.
So either way, you're going
to get the same thing.
And just be very clear, here
we added the exponents.
Because we had the same base
and we're multiplying them.
So we added the exponents.
Here, we multiplied the
exponents because we had
something to an exponent and
then that whole thing being
raised to another exponent.
But regardless of which
direction you go in, as long
as you use your properties in
the correct way, you should
get 9 to the sixth power.