Question

How do you simplify `\frac { ( a + 5b ) ^ { 5} } { ( a + 5b ) ^ { 2} }`?

Answer 1

`(a+5b)^5/(a+5b)^2=(a+5b)^3`

Explanation:

Let's first say that `x=(a+5b)`, so I can write:

`(a+5b)^5/(a+5b)^2=x^5/x^2`

I can use the rule `x^a/x^b=x^(a-b)` to then write:

`x^5/x^2=x^(5-2)=x^3`

Let's now substitute the original expression back in for `x`:

`x^3=(a+5b)^3`