Aspeck of dust in an electron microscope is 1.2x10^2 millimeters wide. the image is 5x10^2 times larger than the actual size. how many millimeters wide is the actual speck of dust?

Let the actual size be x, then
(5 x 10^2)x = 1.2 x 10^2
x = (1.2 x 10^2 / 5 x 10^2) = 0.24 millimeters

Therefore, the actual size is 0.24 millimiters.

Let d be the width of dust seen in electron microscope.
d = 1.2* 10^2 mm

let x be the scaling parameter.
x = 5*10^2mm

dusts actual width D is calculated by scaling d by a factor of x

D = d/x
D =  0.24mm

Note that you are scaling dimensions by a factor of x and not surface of the dust.