## Elementary Technical Mathematics

$\dfrac{1}{10^5}$
Recall the exponent rules: $x^ax^b=x^{a+b}$ $(x^a)^b=x^{ab}$ $\dfrac{x^a}{x^b}=x^{a-b}$ We simplify as follows: $$\frac{(10^3\times10^{-2})^3}{10^3\times10^5}=\frac{(10^1)^3}{10^8}=\frac{10^3}{10^8}=\frac{1}{10^5} .$$