Simplify 3a times a to

the fifth times a squared. So the exponent

property we can use here is if we have the same

base, in this case, it’s a. If we have it raised

to the x power, we’re multiplying it

by a to the y power, then this is just going to

be equal to a to the x plus y power. And we’ll think about why

that works in a second. So let’s just apply it here. Let’s start with the a to

the fifth times a squared. So if we just apply

this property over here, this will result in a to

the fifth plus two-th power. So that’s what those guys

reduce to, or simplify to. And of course, we still

have the 3a out front. Now what I want to do is

take a little bit of an aside and realize why this worked. Let’s think about what a to the

fifth times a squared means. A to the fifth

literally means a times a times a times a times a. Now, a squared literally

means a times a. And we’re multiplying

the two times each other. So we’re multiplying these

five a’s times these two a’s. And what have we just done? We’re multiplying a

times itself five times, and then another two times. We are multiplying

a times itself. So let me make it clear. This over here is

a to the fifth. This over here is a squared. When you multiply

the two, you’re multiplying a by itself

itself seven times. 5 plus 2. So this is a to the seventh

power. a to the 5 plus 2 power. So this simplifies to 3a

times a to the seventh power. Now you might say, how do I

apply the property over here? What is the exponent on the a? And remember, if I just

have an a over here, this is equivalent to

a to the first power. So I can rewrite 3a is 3

times a to the first power. And now it maybe makes

it a little bit clearer. A to the first power– and

the association property of multiplication, I can

do the multiplication of the a’s before I

worry about the 3’s. So I can multiply

these two guys first. So a to the first times

a to the seventh– I just have to add the exponents

because I have the same base and I’m taking the

product– that’s going to be a to

the eighth power. And I still have

this 3 out front. So 3a times a to

the fifth times a squared simplifies to

3a to the eighth power.