The first rule you have to know is
[tex]p^a\cdot p^b = p^{a+b}[/tex]
In other words, if you multiply two powers of the same base, you have to sum the exponents. So, we have
[tex]p^m\cdot p^8=p^{m+8}[/tex]
Which equals [tex]p^{16}[/tex] if and only if [tex]m+8=16[/tex] and thus [tex]m=8[/tex].
The second rule you have to know is
[tex](p^a)^b = p^{ab}[/tex]
In other words, to evaluate the power of a power, you have to multiply the exponents. So, we have
[tex](p^9)^n=p^{9n}[/tex]
Which equals [tex]p^{-27}[/tex] if and only if [tex]9n=-27[/tex] and thus [tex]n=-3[/tex].
Now that we found [tex]m[/tex] and [tex]n[/tex], it's easy to conclude that [tex]m-n=8-(-3)=11[/tex]
