A= \(\dfrac{11}{9}\).\(\dfrac{-3}{2}\)- \(\dfrac{11}{9}\).\(\dfrac{15}{2}\)+(2021)⁰

= \(\dfrac{11}{9}\)(\(\dfrac{-3}{2}\)-\(\dfrac{15}{2}\)) + 1

= \(\dfrac{11}{9}\)(-9) + 1

= -11 + 1

= -10

\(-\frac{2}{3}+\frac{1}{5}.\frac{-10}{7}\\ =-\frac{2}{3}+\frac{1.-10}{5.7}\\ =-\frac{2}{3}+\frac{-2}{7}\\ =-\frac{14}{21}+\frac{-6}{21}\\ =-\frac{20}{21}\)

=\(\frac{-2}{3}+\frac{1}{5}.\frac{-10}{7}\)

=\(\frac{-2}{3}+\frac{-2}{7}\)

=\(\frac{-20}{21}\)

a) \(=\left(13\dfrac{2}{7}+2\dfrac{5}{7}\right):\left(-\dfrac{8}{9}\right)\)

\(=16:\dfrac{-8}{9}=\dfrac{-8\cdot\left(-2\right)\cdot9}{-8}=-18\)

b) 

\(=\left(\dfrac{-6}{11}\cdot\dfrac{11}{-6}\right)\cdot\dfrac{7\cdot10\cdot\left(-2\right)}{10}\)

\(=-14\)

c) \(=\dfrac{-1}{2}\cdot\dfrac{4}{3}\cdot\dfrac{-7}{2}\)

\(=\dfrac{-1\cdot2\cdot2\cdot\left(-7\right)}{2\cdot3\cdot2}=\dfrac{7}{3}\)

a, 35.34 + 35.86 + 65.75 + 65.45

= 35.(34 + 86) + 65.(75 + 45)

= 35.120 + 65.120

= 120.(35+65)

= 120.100

= 12000

b, \(7.5^2-32:2^3+9\)

= 7.25 - 32:8 + 9

= 175 - 4 + 9

= 180

a) 2.5³-3.2+4⁵:4³
= 2.125-6+16
= 250+10
= 260

250-6 + 4^5-3 =>250-6 + 4² =>250-6 + 16 =>260

=260

\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{\left(2^4\right)^3.3^{10}+3.5.2^3.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)

\(=\dfrac{2^{12}.3^{10}+3.5.2^3.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+5.2^{12}.3^{10}}{2^{12}.3^{12}+2^{11}.3^{11}}\)

\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.\left(2.3+1\right)}\)\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.7}=\dfrac{2.2}{7}=\dfrac{4}{7}\)

a) 45.37 + 45.63 - 100

\( 45.(37 + 63) – 100 \)

\(45.100 – 100\)

 \(100.(45 – 1) \)

\( 100 . 44 = 4400\)

a,-9

b,116.42

c,300

d,21

a)\(=45.\left(37+63-\dfrac{20}{9}\right)=45\cdot\dfrac{880}{9}=4400\)

b)\(=148.9-9.48=9.\left(148-48\right)=9.100=900\)

\(a.\left[-\dfrac{6}{11}.\dfrac{11}{-6}\right].\dfrac{7}{10}.\left(-20\right)=1.7.\left(-2\right)=-14\)

\(b.\dfrac{-1}{2}:\dfrac{3}{4}.\dfrac{-7}{2}=\dfrac{7}{4}:\dfrac{3}{4}=\dfrac{7}{3}\)

\(c.\dfrac{93}{7}:-\dfrac{8}{9}+\dfrac{19}{7}:\dfrac{-8}{9}=\left(\dfrac{93}{7}+\dfrac{19}{7}\right):-\dfrac{8}{9}=\dfrac{-9}{8}.\dfrac{112}{7}=-18\)

\(=\dfrac{9}{23}\left(\dfrac{5}{17}-\dfrac{22}{17}\right)+11+\dfrac{9}{23}=11\)