Bài giải:

        $\frac{{{10}^{19}}{{.7}^{21}}}{{{49.14}^{18}}{{.5}^{20}}}+\frac{{{15}^{31}}{{.32}^{5}}}{{{6}^{24}}{{.3}^{7}}{{.5}^{30}}}$

$=\frac{{{(2.5)}^{19}}{{.7}^{21}}}{{{7}^{2}}.{{(2.7)}^{18}}{{.5}^{20}}}+\frac{{{(3.5)}^{31}}.{{({{2}^{5}})}^{5}}}{{{(2.3)}^{24}}{{.3}^{7}}{{.5}^{30}}}$

$=\frac{{{2}^{19}}{{.5}^{19}}{{.7}^{21}}}{{{2}^{18}}{{.7}^{20}}{{.5}^{20}}}+\frac{{{2}^{25}}{{.3}^{31}}{{.5}^{31}}}{{{2}^{24}}{{.3}^{31}}{{.5}^{30}}}$

$=\frac{2.7}{5}+2.5=\frac{64}{5}$

Vậy kết quả của phép tính là: $\frac{64}{5}$