Question

What is `36y^4*.5y^2`?

Please explain, thank you!

Answer 1

The simplified answer is `18y^6`.

Explanation:

Since multiplication is commutative (meaning `3*5` is the same as `5*3`), you can move around the terms, and then combine the constants.

To simplify the `y` terms, use the law of exponents:

`x^color(red)m*x^color(blue)n=x^(color(red)m+color(blue)n)`

Now here's our expression (I added color-coding for each term so it's easier to follow:

`color(white)=36y^4*0.5y^2`

`=color(red)36*color(green)(y^4)*color(blue)0.5*color(magenta)(y^2)`

`=color(red)36*color(blue)0.5*color(green)(y^4)*color(magenta)(y^2)`

`=color(purple)18*color(green)(y^4)*color(magenta)(y^2)`

`=color(purple)18*color(brown)y^(color(green)4+color(magenta)2)`

`=color(purple)18*color(brown)y^color(brown)6`

`=color(purple)18color(brown)y^color(brown)6`

This is the simplified result. Hope this helped!

Answer 2

The answer is `18y^6`, with the explanation below.

Explanation:

A good way to understand what's going on here is to write out all of the multipliers (I'm going to avoid expanding all of the exponents):

`36y^4*0.5y^2=36*y^4*0.5*y^2`

Now, we can start grouping like elements:

`(36*0.5)(y^4*y^2)=18(y^4*y^2)`

As you may or may not know, when you multiply two exponents together with the same base, you simply add the values of the powers together. This way:

`18(y^4*y^2)=18(y^(4+2))`

`color(red)(18y^6)`