$$\frac{{\left({\displaystyle \frac{1}{10}}\right)}^{-3}·{10}^5}{{\left({\displaystyle \frac{1}{1000}}\right)}^3·{1000}^{-5}}$$

$$=\frac{{\left({\displaystyle \frac{10}{1}}\right)}^3·{10}^5}{{\left({\displaystyle \frac{1}{{10}^3}}\right)}^3·{\left({10}^3\right)}^{-5}}$$

$$=\frac{{10}^3·{10}^5}{{\displaystyle \frac{1}{{10}^9}}·{10}^{-15}}$$

$$=\frac{{10}^8}{{\displaystyle {10}^{-9}}·{10}^{-15}}$$

$$=\frac{{10}^8}{{\displaystyle {10}^{-24}}}$$

$$={10}^{8-\left(-24\right)}$$