$$\frac { 8r^{ 1/2 }s^{ -3 } }{ 2r^{ -2 }s^{ 4 } } $$
The first step I took was getting rid of the negative exponents:
$$\frac { 8r^{ 1/2 }2r^{ 2 } }{ s^{ 3 }s^{ 4 } } $$
Then I performed the multiplication in the numerator and denominator and got:
$$\frac { 16r^{ 5/2 } }{ s^{ 7 } } $$
Apparently, this is wrong. What mistake did I make?
You forgot to take the reciprocal of $2$ in the denominator. So, the answer is $4r^{5/2}/s^7$.