Answer
The average power output of the insect is 0.196 W.
Work Step by Step
We can find the work for each downward stroke.
$Work = F~d = 2mg~d$
$Work = (2)(0.010~kg)(9.80~m/s^2)(0.010~m)$
$Work = 0.00196~J$
We can use the work to find the power.
$P = 100\times (0.00196~J)/s$
$P = 0.196~W$
The average power output of the insect is 0.196 W.