Question

Can someone plez help me I’m a freshman and this is homework

Answer 1

`40m^4n^(10)` units is the area of the triangle

Skills needed: Combining Like Terms, Triangle Area

Explanation:

1) First, let's understand two important concepts:

---> The area of a triangle:

`(1)/(2) * b * h` is the area

The base is one of the sides of the triangle, and the height is perpendicular to the base and connects to a vertex usually opposite of the base.

Perpendicular means to intersect at a right angle (that square thing that is drawn into the diagram signifies a right angle).

---> Combining Like Exponent Terms

Let's say we have:
`a^b` and
`a^c`

If we are multiplying, we are doing
`a^b * a^c`

`a^b*a^c=a^(b+c)`

Example:
`2^4*2^2=2^(4+2)=2^6`

Think about it: 2 to the 4th power is 16, and 2 squared is 4. When multiplying those together you get 16 * 4 = 64. The method above yields the same answer.

2) Now, let's apply these two concepts to the problem shown. We are given a base (
`20m^3n^5`) and a height perpendicular to the base (
`4mn^5`).

---> Let's substitute in for the formula:
`(1)/(2) * 20m^3n^5 * 4mn^5`

Let's combine like terms now:

`(1)/(2) * 20 * 4` can be combined and multiplied as they are all constant numbers.

`(1)/(2) * 20 * 4 = 10 * 4 = 40`

Now let's combine the exponent parts

We can split into two groups for the two different variables (
`m, n`)

--->
`m^3*m` can be combined (remember
`m = m^1`) -->
`m^3*m=m^3*m^1=m^4`

--->
`n^5*n^5` can be combined -->
`n^5*n^5=n^(10)`

So we have:
`40*m^4*n^(10)` as the answer.

You can take out the multiplication signs:
`40m^4n^(10)`

(When you have unlike terms, you do not need to separate with multiplication signs)