How Do You Solve a Word Problem by Dividing Monomials?

A ratio can be represented as a fraction, so for us the fraction is the height divided by the base
Use the associative property to move the variables around in the denominator
Split up the variables so that each variable has its own fraction by itself
Instead of dividing variables, you can just subtract their exponents to find the answer

1. The height is 32a³b⁷c²
2. The base is 4ac⁴b⁵
3. 'a', 'b', and 'c' are variables
1. The height is 32a³b⁷c²
2. The base is 4ac⁴b⁵
3. 'a', 'b', and 'c' are variables
1. The ratio is 32a³b⁷c² over 4ac⁴b⁵
2. 'a', 'b', and 'c' are variables
1. 'a', 'b', and 'c' are variables
1. 'a', 'b', and 'c' are variables
2. Originally the denominator has the variables in the order, a, c, b
3. We switch the b⁵ and c⁴ variables so that the order is now a, b, and c
1. 'a', 'b', and 'c' are variables
2. We are making each variable its own fraction, so that they will be easier to cancel out
1. Instead of dividing variables you can use the quotient of powers to just subtract their exponents to find the answer
1. So a^3-1 is the same as dividing a³ by a
2. 'a' is a variable
1. So b^7-5 is the same as dividing b⁷ by b⁵
2. 'b' is a variable
1. So c^2-4 is the same as dividing c² by c⁴
2. 'c' is a variable
1. 'a', 'b', and 'c' are variables
2. c^-2 is another way of writing 1 divided by c²

Calculate the ratio of the height to the base for the triangle in the diagram. Write your answer as a monomial in simplest form.