Exponent Properties 1

u11_l1_t2_we1 Exponent Properties 1

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 and 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, and 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 five plus (2nd) power.

so that's what those guys reduce to or simplify to

and of course we still have, we still have the

3a out front.

Now, what I want to do to take a little bit to the side

and realize why this works.

Let's think about 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,

so what have we just done?

We're multiplying a by itself five times, then

another two times, 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 seven times! Five plus two!

So this is a to the seventh power. (A to the five plus two 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 as three times a to the first power

And now maybe it makes it a little bit more clearer

a to the first power, and the association property

of multiplication-- I can do the multiplication of

the a's first 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 cause 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 three out front.

So, 3a times a to the fifth times a squared simplifies to

3a to the eighth power.