Đáp án:
$\begin{array}{l}
1)a)0,5 + \dfrac{4}{9} - \dfrac{{21}}{{35}} + \dfrac{5}{9} - \dfrac{{14}}{{35}}\\
= 0,5 + \left( {\dfrac{4}{9} + \dfrac{5}{9}} \right) + \left( {\dfrac{{ - 21}}{{35}} - \dfrac{{14}}{{35}}} \right)\\
= 0,5 + \dfrac{9}{9} + \dfrac{{ - 35}}{{35}}\\
= 0,5 + 1 - 1\\
= 0,5\\
b)0,9.\sqrt {100} - \sqrt {\dfrac{1}{9}} \\
= 0,9.10 - \dfrac{1}{3}\\
= 9 - \dfrac{1}{3}\\
= \dfrac{{26}}{3}\\
c)\dfrac{{{2^{30}}{{.9}^8}}}{{{6^{12}}{{.8}^6}}} = \dfrac{{{2^{30}}{{.3}^{16}}}}{{{2^{12}}{{.3}^{12}}{{.2}^{18}}}}\\
= \dfrac{{{2^{30}}{{.3}^{16}}}}{{{2^{30}}{{.3}^{12}}}}\\
= {3^4}\\
= 243\\
2)a)\left( {\dfrac{5}{7} - x} \right).\dfrac{{11}}{{15}} = \dfrac{{ - 22}}{{45}}\\
\Rightarrow \left( {\dfrac{5}{7} - x} \right) = - \dfrac{{22}}{{45}}.\dfrac{{15}}{{11}}\\
\Rightarrow \dfrac{5}{7} - x = \dfrac{{ - 2}}{3}\\
\Rightarrow x = \dfrac{5}{7} - \left( { - \dfrac{2}{3}} \right)\\
\Rightarrow x = \dfrac{5}{7} + \dfrac{2}{3}\\
\Rightarrow x = \dfrac{{15 + 14}}{{21}}\\
\Rightarrow x = \dfrac{{29}}{{21}}\\
Vậy\,x = \dfrac{{29}}{{21}}\\
b)\left| {x + \dfrac{1}{3}} \right| - 5 = 6\\
\Rightarrow \left| {x + \dfrac{1}{3}} \right| = 11\\
\Rightarrow \left[ \begin{array}{l}
x + \dfrac{1}{3} = 11\\
x + \dfrac{1}{3} = - 11
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 11 - \dfrac{1}{3} = \dfrac{{32}}{3}\\
x = - 11 - \dfrac{1}{3} = \dfrac{{ - 34}}{3}
\end{array} \right.\\
Vậy\,x = \dfrac{{32}}{3};x = \dfrac{{ - 34}}{3}\\
c)\dfrac{{2x}}{{15}} = \dfrac{{ - 6}}{{25}}\\
\Rightarrow x = \dfrac{{ - 6}}{{25}}.\dfrac{{15}}{2}\\
\Rightarrow x = \dfrac{{ - 9}}{5}\\
Vậy\,x = \dfrac{{ - 9}}{5}
\end{array}$
