a) \(\sqrt{\dfrac{25}{81}.\dfrac{16}{49}.\dfrac{196}{9}}=\sqrt{\dfrac{25}{81}}.\sqrt{\dfrac{16}{49}}.\sqrt{\dfrac{196}{9}}=\dfrac{5}{9}.\dfrac{4}{7}.\dfrac{14}{3}=\dfrac{40}{27}\)

b) \(\sqrt{3\dfrac{1}{16}.2\dfrac{14}{25}.2\dfrac{34}{81}}=\sqrt{\dfrac{49}{16}.\dfrac{64}{25}.\dfrac{196}{81}}=\sqrt{\dfrac{49}{16}}.\sqrt{\dfrac{64}{25}}.\sqrt{\dfrac{196}{81}}=\dfrac{7}{4}.\dfrac{8}{5}.\dfrac{14}{9}=\dfrac{196}{45}\)

c) \(\dfrac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}=\sqrt{\dfrac{640.34,3}{567}}=\sqrt{\dfrac{64.49}{81}}=\dfrac{\sqrt{64}.\sqrt{49}}{\sqrt{81}}=\dfrac{8.7}{9}=\dfrac{56}{9}\)

d) \(\sqrt{21,6}.\sqrt{810}.\sqrt{11^2-5^2}=\sqrt{21,6.810.\left(11^2-5^2\right)}=\sqrt{216.81.\left(11+5\right)\left(11-5\right)}=\sqrt{36^2.9^2.4^2}=36.9.4=1296\)

\(A=\frac{1}{2}+\frac{-1}{7}-\frac{-1}{13}+\frac{-1}{13}-\frac{-2}{5}+\frac{-11}{21}+\frac{1}{10}\)

\(A=\frac{5}{10}-\frac{3}{21}+\frac{1}{13}-\frac{1}{13}+\frac{4}{10}-\frac{11}{21}+\frac{1}{10}\)

\(A=\left(\frac{5+4+1}{10}\right)+\left(\frac{-3}{21}-\frac{11}{21}\right)+\left(\frac{1}{13}-\frac{1}{13}\right)\)

\(A=1+\frac{-2}{3}=\frac{3-2}{3}=\frac{1}{3}\)

a: ĐKXĐ: \(x\notin\left\{0;-5\right\}\)

a) \(\dfrac{40}{27}\)

b) \(\dfrac{196}{45}\)

c) \(\dfrac{56}{9}\)

d) 1296

a) $\sqrt{\genfrac{}{}{0ex}{}{25}{81}\cdot \genfrac{}{}{0ex}{}{16}{49}\cdot \genfrac{}{}{0ex}{}{196}{9}}$

$=\sqrt{\genfrac{}{}{0ex}{}{25}{81}}\cdot \sqrt{\genfrac{}{}{0ex}{}{16}{49}}\cdot \sqrt{\genfrac{}{}{0ex}{}{196}{9}}$

$=\sqrt{{\left(\genfrac{}{}{0ex}{}{5}{9}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{4}{7}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{14}{3}\right)}^2}$

$=\genfrac{}{}{0ex}{}{5}{9}\cdot \genfrac{}{}{0ex}{}{4}{7}\cdot \genfrac{}{}{0ex}{}{14}{3}=\genfrac{}{}{0ex}{}{40}{27}$.

b) $\sqrt{3\genfrac{}{}{0ex}{}{1}{16}\cdot 2\genfrac{}{}{0ex}{}{14}{25}\cdot 2\genfrac{}{}{0ex}{}{34}{81}}$

$=\sqrt{\genfrac{}{}{0ex}{}{49}{16}\cdot \genfrac{}{}{0ex}{}{64}{25}\cdot \genfrac{}{}{0ex}{}{196}{81}}$

$=\sqrt{\genfrac{}{}{0ex}{}{49}{16}}\cdot \sqrt{\genfrac{}{}{0ex}{}{64}{25}}\cdot \sqrt{\genfrac{}{}{0ex}{}{196}{81}}$

$=\sqrt{{\left(\genfrac{}{}{0ex}{}{7}{4}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{8}{5}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{14}{9}\right)}^2}$

$=\genfrac{}{}{0ex}{}{7}{4}\cdot \genfrac{}{}{0ex}{}{8}{5}\cdot \genfrac{}{}{0ex}{}{14}{9}=\genfrac{}{}{0ex}{}{196}{45}$.

c) $\genfrac{}{}{0ex}{}{\sqrt{640}\cdot \sqrt{34,3}}{\sqrt{567}}=\sqrt{\genfrac{}{}{0ex}{}{640.34,3}{567}}=\sqrt{\genfrac{}{}{0ex}{}{64.343}{567}}$

$=\sqrt{\genfrac{}{}{0ex}{}{64.49.7}{81.7}}=\sqrt{\genfrac{}{}{0ex}{}{64.49}{81}}$

$=\genfrac{}{}{0ex}{}{\sqrt{64}\cdot \sqrt{49}}{\sqrt{81}}=\genfrac{}{}{0ex}{}{8.7}{9}$

$=\genfrac{}{}{0ex}{}{56}{9}$.

d) $\sqrt{21,6}\cdot \sqrt{810}\cdot \sqrt{11^2-5^2}$

$=\sqrt{21,6.810\cdot \left(11^2-5^2\right)}$

$=\sqrt{216.81.(11+5)(11-5)}$

$=\sqrt{36.6.9^2\cdot 4^2.6}$

$=\sqrt{36^2.9^2\cdot 4^2}=36.9.4=1296$.