Tính các biểu thức sau:

i) $27\dfrac{1}{4}.\dfrac{5}{8}-13\dfrac{1}{4}.\dfrac{5}{8}$.

ii) $2\Big| \dfrac{1}{2}-\dfrac{3}{4} \Big|+\sqrt{\dfrac{4}{9}}$.

Tính giá trị các biểu thức:

i) $16\dfrac{3}{5}\Big(-\dfrac{1}{3} \Big)+13\dfrac{3}{5}.\sqrt{\dfrac{1}{9}}$;

ii) $\dfrac{5}{15}+\dfrac{14}{25}-\dfrac{12}{9}+\dfrac{2}{7}-\dfrac{-11}{25}$.

Thực hiện phép tính:

i) $\dfrac{-2}{7}.3\dfrac{5}{8}-2\dfrac{5}{8}.\dfrac{-2}{7}$;

ii) $-3.\Big| \dfrac{1}{2}-\dfrac{3}{4} \Big|+\sqrt{\dfrac{25}{36}}$.

Tính giá trị biểu thức: $A=\Big(\dfrac{10.\sqrt{1,44}}{3}+\dfrac{24.\sqrt{0,25}}{7} \Big)\, : \, \Big(\dfrac{12}{7}+\dfrac{\sqrt{144}}{9} \Big)$.

Thực hiện phép tính:

i) $\Big[ \Big(\dfrac{2}{191}-\dfrac{3}{382} \Big). \dfrac{191}{17}+\dfrac{33}{34} \Big]\, : \, \Big[ \Big(\dfrac{7}{1\,011}+\dfrac{11}{2\,022} \Big). \dfrac{1\,011}{25}+\dfrac{9}{2} \Big]$.

ii) $\sqrt{{{11}^{2}}-72}-1\dfrac{1}{2}\, : \, \sqrt{\dfrac{25}{4}}-{{\Big(\dfrac{2\,023}{2\,024} \Big)}^{0}}$.

Tính giá trị các biểu thức sau:

$A=\dfrac{1}{2}. \dfrac{1}{-3}+\dfrac{1}{-3}. \dfrac{1}{4}+\dfrac{1}{4}. \dfrac{1}{-5}+\dfrac{1}{-5}. \dfrac{1}{6}$.

$B=3\sqrt{{{\Big(-5 \Big)}^{2}}}-0,5.0,(3).\sqrt{9}+\Big| -\dfrac{{{2}^{2}}}{3} \Big|\, : \, \Big(-1\dfrac{1}{3} \Big)$.

Thực hiện phép tính:

a) $\sqrt{1+\dfrac{9}{16}}:{{\Big(\dfrac{1}{4}-\dfrac{1}{3} \Big)}^{2}}+\sqrt{1-\dfrac{80}{81}}:{{\Big(\dfrac{1}{3}-\dfrac{1}{2} \Big)}^{2}}$;

b) $\dfrac{{{25}^{5}}{{.7}^{3}}-{{5}^{10}}{{.49}^{2}}}{{{125}^{3}}{{.7}^{3}}+{{5}^{9}}{{.14}^{3}}}$.

Thực hiện các phép tính:

a) $B=\dfrac{{{\Big(\dfrac{2}{5} \Big)}^{7}}{{.5}^{7}}+{{\Big(\dfrac{9}{4} \Big)}^{3}}:{{\Big(\dfrac{3}{16} \Big)}^{3}}}{{{2}^{7}}{{.5}^{2}}+512}$;

b) $C=\left| \dfrac{7}{9}-\dfrac{\dfrac{1}{3}-\dfrac{2}{5}-\dfrac{3}{7}}{\dfrac{9}{3}-\dfrac{18}{5}-\dfrac{27}{7}} \right|-\left| \dfrac{8}{9}-{{\Big(\dfrac{\sqrt{2}}{3} \Big)}^{2}} \right|$.

Tính giá trị của các biểu thức:

a) $A=\sqrt{{{11}^{2}}-72}-1\dfrac{1}{2}:\sqrt{\dfrac{25}{4}}-{{\Big(\dfrac{2\,022}{2\,023} \Big)}^{0}}$;

b) $B=\dfrac{{{4}^{6}}{{.9}^{5}}+{{6}^{9}}.120}{{{8}^{4}}{{.3}^{12}}-{{6}^{11}}}.$

Rút gọn biểu thức sau: $A=\dfrac{{{\Big(\dfrac{2}{3} \Big)}^{3}}.\sqrt{{{\Big(-\dfrac{3}{4} \Big)}^{4}}}.{{\Big(-1 \Big)}^{2\,023}}}{{{\Big(\dfrac{2}{5} \Big)}^{2}}.{{\Big(\dfrac{-5}{12} \Big)}^{3}}}-\dfrac{71}{5}$.