You would solve it in two parts.
4*n = 44 Divide by 4
4n/4 = 44/4
n = 11
=============
z^m * z^2 = z^9
When the bases are the same (on the left) the powers on the left add
m + 2
The powers on the left side of the equation are the same as the powers on the right when the bases are the same.
m + 2 = 9 Subtract 2 from both sides.
m + 2 - 2 = 9 - 2
m = 7
=================
Answers
m = 7
n = 11