Answer:
[tex]40m^4n^{10}[/tex] units is the area of the triangle
Skills needed: Combining Like Terms, Triangle Area
Step-by-step explanation:
1) First, let's understand two important concepts:
---> The area of a triangle:
[tex]\frac{1}{2} * b * h[/tex] 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: [tex]a^b[/tex] and [tex]a^c[/tex]
If we are multiplying, we are doing [tex]a^b * a^c[/tex]
[tex]a^b*a^c=a^{b+c}[/tex]
Example: [tex]2^4*2^2=2^{4+2}=2^6[/tex]
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 ([tex]20m^3n^5[/tex]) and a height perpendicular to the base ([tex]4mn^5[/tex]).
---> Let's substitute in for the formula: [tex]\frac{1}{2} * 20m^3n^5 * 4mn^5[/tex]
Let's combine like terms now:
[tex]\frac{1}{2} * 20 * 4[/tex] can be combined and multiplied as they are all constant numbers.
[tex]\frac{1}{2} * 20 * 4 = 10 * 4 = 40[/tex]
Now let's combine the exponent parts
We can split into two groups for the two different variables ([tex]m, n[/tex])
---> [tex]m^3*m[/tex] can be combined (remember [tex]m = m^1[/tex]) --> [tex]m^3*m=m^3*m^1=m^4[/tex]
---> [tex]n^5*n^5[/tex] can be combined --> [tex]n^5*n^5=n^{10}[/tex]
So we have: [tex]40*m^4*n^{10}[/tex] as the answer.
You can take out the multiplication signs: [tex]40m^4n^{10}[/tex]
(When you have unlike terms, you do not need to separate with multiplication signs)
