\(1\dfrac{1}{2}x1\dfrac{1}{3}x1\dfrac{1}{4}x1\dfrac{1}{5}x1\dfrac{1}{6}x1\dfrac{1}{7}x1\dfrac{1}{8}x1\dfrac{1}{9}\)

\(=\dfrac{3}{2}x\dfrac{4}{3}x\dfrac{5}{4}x\dfrac{6}{5}x\dfrac{7}{6}x\dfrac{8}{7}x\dfrac{9}{8}x\dfrac{10}{9}\)

\(=x^7.\dfrac{3.4.5.6.7.8.9.10}{2.3.4.5.6.7.8.9}\)

\(=x^7.\dfrac{10}{2}\)

\(=5x^7\)

\(=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times...\times\dfrac{9}{8}\times\dfrac{10}{9}=\dfrac{10}{2}=5\)

a) \(5^6:5^5+\left(\dfrac{4}{9}\right)^0=5^{6-5}+1=5+1=6\)

b) \(\left(\dfrac{3}{7}\right)^{21}:\left(1-\dfrac{40}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^6\)

\(=\left(\dfrac{3}{7}\right)^{21-6}=\left(\dfrac{3}{7}\right)^{15}\)

c) \(\left(\dfrac{2}{3}\right)^3-\left(\dfrac{-52}{3}\right)^0+\dfrac{4}{9}\)

\(=\dfrac{8}{27}-1+\dfrac{4}{9}\)

\(=\dfrac{8-27+12}{27}=-\dfrac{7}{27}\)

\(a)5^6:5^5+\left(\dfrac{4}{9}\right)^0=5^1+1=6\)

\(b,\left(\dfrac{3}{7}\right)^{21}:\left(1-\dfrac{40}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{49-40}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^3=\left(\dfrac{3}{7}\right)^{21}:[\left(\dfrac{3}{7}\right)^2]^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^6=\left(\dfrac{3}{7}\right)^{21-6}\)

\(=\left(\dfrac{3}{7}\right)^{15}\)

\(c,3.\left(\dfrac{2}{3}\right)^3-\left(\dfrac{-52}{3}\right)^0+\dfrac{4}{9}\)

\(=3.\dfrac{8}{27}-1+\dfrac{4}{9}\)

\(=\dfrac{8}{9}-1+\dfrac{4}{9}\)

\(=\dfrac{8-9+4}{9}=\dfrac{1}{3}\)

a) 56:55+(49)0=56−5+1=5+1=656:55+(94​)0=56−5+1=5+1=6

b) (37)21:(1−4049)3(73​)21:(1−4940​)3

=(37)21:(949)3=(73​)21:(499​)3

=(37)21:[(37)2]3=(73​)21:[(73​)2]3

=(37)21:(37)6=(73​)21:(73​)6

=(37)21−6=(37)15=(73​)21−6=(73​)15

c) (23)3−(−523)0+49(

\(\dfrac{4}{9}+\dfrac{5}{8}\)=\(\dfrac{32}{72}+\dfrac{45}{72}=\dfrac{77}{72}\)

\(\dfrac{6}{10}+\dfrac{9}{2}=\dfrac{6}{10}+\dfrac{45}{10}=\dfrac{51}{10}\)

\(\dfrac{10}{2}-\dfrac{5}{2}=\dfrac{5}{2}\)

\(\dfrac{8}{8}x1=\dfrac{8}{8}x\dfrac{1}{1}=\dfrac{8}{8}\)

a: \(=\dfrac{-8}{9}-\dfrac{6}{5}+\dfrac{8}{9}=-\dfrac{6}{5}\)

c: \(=\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}\)

\(...=\dfrac{5+6+9+11+10+55+4}{8}=\dfrac{100}{8}=\dfrac{25}{2}\)

\(\dfrac{5+6+9+11+10+55+4}{8}=\dfrac{100}{8}\)

\(\dfrac{100}{8}\) rút gọn được nhé bnn.

\(E=\dfrac{98:\left(\dfrac{4}{5}\cdot\dfrac{5}{4}\right)}{\dfrac{16}{25}-\dfrac{1}{25}}+\dfrac{\left(\dfrac{27}{25}-\dfrac{2}{25}\right)\cdot\dfrac{7}{4}}{\left(\dfrac{59}{9}-\dfrac{13}{4}\right)\cdot\dfrac{36}{17}}\\ E=\dfrac{98}{\dfrac{3}{5}}+\dfrac{\dfrac{7}{4}}{\dfrac{119}{36}\cdot\dfrac{36}{17}}\\ E=\dfrac{490}{3}+\dfrac{\dfrac{7}{4}}{7}=\dfrac{490}{3}+\dfrac{1}{4}=\dfrac{1963}{12}\)

\(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

\(=\left(\dfrac{1}{10}+\dfrac{9}{10}\right)+\left(\dfrac{2}{10}+\dfrac{8}{10}\right)+\left(\dfrac{3}{10}+\dfrac{7}{10}\right)+\left(\dfrac{4}{10}+\dfrac{6}{10}\right)+\dfrac{5}{10}\)

\(=1+1+1+1+\dfrac{5}{10}\)

\(=4+\dfrac{5}{10}\)

\(=\dfrac{45}{10}\)

\(13,25:0,5+13,25:0,25+13,25:0,125+13,25\times6\)

\(=13,25:\dfrac{1}{2}+13,25:\dfrac{1}{4}+13,25:\dfrac{1}{8}+13,25\times6\)

\(=13,25\times2+13,25\times4+13,25\times8+13,25\times6\)

\(=13,25\times\left(2+4+8+6\right)\)

\(=13,25\times20\)

\(=265\)

Câu 1:

\(-\dfrac{5}{7}\cdot\dfrac{7}{-45}=\dfrac{1}{9}\) ; \(-\dfrac{3}{10}\cdot-30=9\) ; \(-12\cdot-\dfrac{2}{36}=\dfrac{2}{3}\)

Caau2;3;4;5,... tự bấm máy tính là ra