The given rational function is
[tex]\frac{16m^2}{24m^7}[/tex]To simplify it we will divide 16 and 24 by their greatest common factor and subtract the powers of m
[tex]16\rightarrow1\times16,2\times8,4\times4[/tex]Then the factors of 16 are 1, 2, 4, 8, 16
[tex]24\rightarrow1\times24,2\times12,3\times8,4\times6[/tex]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
[tex]\begin{gathered} \frac{16m^2}{24m^7}= \\ \\ \frac{\frac{16}{8}m^2}{\frac{24}{8}m^7}= \\ \\ \frac{2m^2}{3m^7} \end{gathered}[/tex]Now, we will subtract the powers of m
[tex]\frac{2m^2}{3m^7}=\frac{2}{3}m^{2-7}=\frac{2}{3}m^{-5}[/tex]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
[tex]\frac{2}{3}m^{-5}=\frac{2}{3m^5}[/tex]The answer is
[tex]\frac{16m^2}{24m^7}=\frac{2}{3m^5}[/tex]