Question

Rational Functions 16m^2———-24m^7(Simplify)

Answer 1

The given rational function is

`(16m^2)/(24m^7)`

To simplify it we will divide 16 and 24 by their greatest common factor and subtract the powers of m

`16\rightarrow1*16,2*8,4*4`

Then the factors of 16 are 1, 2, 4, 8, 16

`24\rightarrow1*24,2*12,3*8,4*6`

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

The common factors of 16 and 24 are 1, 2, 4, 8

The greatest one is 8

Then we will divide 16 and 24 by 8 to simplify the fraction

`\begin{gathered} (16m^2)/(24m^7)= \\ \\ ((16)/(8)m^2)/((24)/(8)m^7)= \\ \\ (2m^2)/(3m^7) \end{gathered}`

Now, we will subtract the powers of m

`(2m^2)/(3m^7)=(2)/(3)m^(2-7)=(2)/(3)m^(-5)`

To put the fraction in the simplest form we will write m^-5 by a positive power by changing its place from up to downing

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

The answer is

`(16m^2)/(24m^7)=(2)/(3m^5)`