I know that each time you go up an exponent, you multiply by the base again e.g. $2^2$ to $2^3$. To go down, you you divide by the base. The way I find negative exponents is that I divide 1 by the base^exponent
E.g.
$10^{-3} =$ ?
$10^0 = 1$
$1 ÷ 10 = 0.1$
$0.1 ÷ 10 = 0.01$
$0.01 ÷ 10 = 0.001$
$10^{-3} = 0.001$
The fraction is $\frac{1}{1000}$.
Did I understand this correctly?