Question

How do you simplify `(12mn)/( 12m^3n^5)` using only positive exponents?

Answer 1

Subtract the exponents in the denominator from the exponents in the numerator.

Explanation:

Before we do anything, we can divide 12 by 12 and get rid of those numbers. We now have `(mn)/(m^3n^5)`.

Next, we can use the rule that says `x^a/x^b=x^(a-b)`. To make this easier, let's separate the fraction we have into two fractions:

`m/m^3=m^(1-3)=m^-2=1/m^2`
`n/n^5=n^(1-5)=n^-4=1/n^4`

We can now combine the two fractions together to get our answer, which is `1/(m^2n^4)`.