1) $-\dfrac{1}{2}-(2\dfrac{5}{8}-\dfrac{1}{3})$
$=-\dfrac{1}{2}-\dfrac{21}{8}+\dfrac{1}{3}$
$=-\dfrac{12}{24}-\dfrac{63}{24}+\dfrac{8}{24}=-\dfrac{43}{24}$
2) $-\dfrac{1}{75}-(-\dfrac{1}{9}-2\dfrac{1}{18})$
$=-\dfrac{1}{75}-(-\dfrac{2}{18}-\dfrac{37}{18})$
$=-\dfrac{1}{75}+\dfrac{13}{6}=\dfrac{109}{50}$
3) $-\dfrac{5}{6}-(-\dfrac{3}{8}+\dfrac{1}{10})$
$=-\dfrac{5}{6}+\dfrac{3}{8}+\dfrac{1}{10}$
$=-\dfrac{11}{24}+\dfrac{1}{10}=-\dfrac{110}{240}+\dfrac{24}{240}=-\dfrac{43}{120}$
4) $\dfrac{2}{5}+(-\dfrac{4}{3})+(-\dfrac{1}{2})$
$=\dfrac{2}{5}-\dfrac{4}{3}-\dfrac{1}{2}$
$=\dfrac{12}{30}-\dfrac{40}{30}-\dfrac{15}{30}=-\dfrac{43}{30}$
5) $\dfrac{3}{12}-(\dfrac{6}{15}-\dfrac{3}{10})$
$=\dfrac{3}{12}-\dfrac{1}{10}$
$=\dfrac{30}{120}-\dfrac{12}{120}=\dfrac{3}{20}$
6) $\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{(2^3)^5.9^4}{(6^2)^3.8^3}$
$=\dfrac{8^5.9^4}{8^3.36^3}=\dfrac{8^5}{8^3}.\dfrac{9^4}{36^3}$
$=8^2.\dfrac{9}{64}=64.\dfrac{9}{64}=9$
