If you need to, you can write and solve an equation for the factor you seek.
... 6×10^10 = factor × 2×10^-3
Divide by 2×10^-3 to find the value of the factor:
... (6×10^10)/(2×10^-3) = factor
... factor = (6/2)×10^(10-(-3))
... factor = 3×10^13
The first number is 3×10^13 times the second number.
_____
An exponent signifies repeated multiplication.
... 10×10×10 = 10³
Just as you cancel common factors when you do division, you can subtract exponents.
The same process works regardless of the signs of the exponents. When multiplying, we add exponents; when dividing we subtract the exponent of the denominator.