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a² - n² = (a + n)(a - n)

a) \(\left(3^{35}+3^{34}-3^{33}\right):3^{32}\)

\(=\frac{3^{35}}{3^{32}}+\frac{3^{34}}{3^{32}}-\frac{3^{33}}{3^{32}}\)

\(=3^3+3^2-3\)

\(=27+9-3\)

\(=33\)

b) \(5^3.37+5^3.64-5^7:5^4\)

\(=5^3.37+5^3.64-5^3\)

\(=5^3\left(37+64-1\right)\)

\(=5^3.100\)

\(=125.100\)

\(=12500\)

\(\left(3^{35}+3^{34}-3^{33}\right)\div3^{32}=3^{33}\left(3^2+3-1\right)\div3^{32}\)

\(=3^{33}.11\div3^{32}=11\left(3^{33-32}\right)=11.3=33\)

 Ê Despacito, tai sao ở chỗ:

= 5³ x 37 + 5³ x 64 - 5³

= 5³ x ( 37 + 64 - 1)

Tại sao 5³ lai = 1

2−3+5−[−12+5−(−3+7)−12]+322−3+5−[−12+5−(−3+7)−12]+32

=2−8−[−7−4−12]+32=2−8−[−7−4−12]+32

=2−8+23+32=2−8+23+32

=2−63=2−63

=−61

7)\(\dfrac{-19}{34}\left(\dfrac{17}{19}+\dfrac{49}{18}\right)+\dfrac{49}{18}\left(\dfrac{19}{34}-\dfrac{18}{7}\right)\)

=\(\dfrac{-19}{34}.\dfrac{17}{19}+\dfrac{49}{18}.\dfrac{-19}{34}+\dfrac{49}{18}.\dfrac{19}{34}-\dfrac{18}{7}.\dfrac{49}{18}\)

=\(\dfrac{1}{2}+\left(\dfrac{49}{18}.\dfrac{-19}{34}+\dfrac{49}{18}.\dfrac{19}{34}\right)-7\)

=\(\dfrac{1}{2}+\left[\dfrac{49}{18}\left(\dfrac{-19}{34}+\dfrac{19}{34}\right)\right]-7\)

=\(\dfrac{1}{2}+0-7=\dfrac{-13}{2}\)

8)\(\dfrac{29}{32}\left(\dfrac{41}{36}-\dfrac{32}{58}\right)-\dfrac{41}{36}\left(\dfrac{29}{32}+\dfrac{18}{41}\right)\)

=\(\dfrac{29}{32}.\dfrac{41}{36}-\dfrac{29}{32}.\dfrac{32}{58}-\dfrac{41}{36}.\dfrac{29}{32}+\dfrac{18}{41}.\dfrac{41}{36}\)

=\(\left(\dfrac{29}{32}.\dfrac{41}{36}-\dfrac{41}{36}\dfrac{29}{32}\right)-\dfrac{29}{32}.\dfrac{32}{58}+\dfrac{18}{41}.\dfrac{41}{36}\)

=\(0-\dfrac{1}{2}+\dfrac{1}{2}=0\)

Ta có : [ ( 2/193 - 3/386 ) * 193/17 + 32/34 ] : [ ( 7/2001 + 11/4002 ) * 2001/25 + 9/2 ] .

=> [ 2/193 * 193/17 - 3/386 * 193/17 + 32/34 ] : [ 7/2001 * 2001/25 + 11/4002 * 2001/25 + 9/2 ] .

=> [ 2/17 - 3/34 + 32/34 ] : [ 7/25 + 11/50 + 9/2 ] .

=> [ 4/34 - 3/34 + 32/34 ] : [ 14/50 + 11/50 + 225/50 ] .

=> 33/34 : 5 .

=> 33/34 * 1/5 .

=> 33/170 .

Tính bằng cách thuận tiện nhất:

\(=\left[\left(\frac{2}{193}\cdot\frac{193}{17}\right)-\left(\frac{3}{386}\cdot\frac{193}{17}\right)+\frac{32}{34}\right]:\left[\left(\frac{7}{2001}\cdot\frac{2001}{25}\right)+\left(\frac{11}{4002}\cdot\frac{2001}{25}\right)+\frac{9}{2}\right]\)

\(=\left[\left(\frac{2}{17}-\frac{3}{17}\right)+\frac{32}{34}\right]:\left[\left(\frac{7}{25}+\frac{11}{50}\right)+\frac{9}{2}\right]\)

\(=\left(-\frac{1}{17}+\frac{32}{34}\right):\left(\frac{1}{2}+\frac{9}{2}\right)\)

\(=\frac{15}{17}+5\)

\(=\frac{100}{17}\)

~ học tốt ~

\(\frac{11\cdot3^{32}\cdot3^8-9^{15}\cdot3}{\left(2\cdot3^{15}\right)^2}\)

\(=\frac{11\cdot3^{40}-3^{30}\cdot3}{2^2\cdot3^{30}}\)

\(=\frac{11\cdot3^{40}-3^{31}}{2^2\cdot3^{30}}\)

\(=\frac{3^{31}\cdot\left(11\cdot3^{19}-1\right)}{2^2\cdot3^{30}}\)

\(=\frac{3\cdot\left(11\cdot3^{19}-1\right)}{2^2}\)

ai tính nhanh được tiếp thì giải ra mik xem vs

`1, (10-4-6)+(5/4-9/14-5/7+7/3)

=0+187/84

=187/ 84

29/32.41/36-29/32.32/58-41/36.29/32-41/36.18/41

=-29/32.32/58-41/36.18/41

=-1/2-1/2=-1

\(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+....+\frac{1}{32}\left(1+2+3+...+32\right)\)

\(=1+\frac{1}{2}.\frac{2\left(2+1\right)}{2}+\frac{1}{3}.\frac{3\left(3+1\right)}{2}+....+\frac{1}{32}.\frac{32.\left(32+1\right)}{2}\)

\(=1+\frac{2+1}{2}+\frac{3+1}{2}+....+\frac{32+1}{2}\)

\(=1+\frac{3}{2}+\frac{4}{2}+....+\frac{33}{2}\)

\(\frac{2+3+4+....+33}{2}\)

\(=\frac{\frac{33\left(33+1\right)}{2}-1}{2}=280\)

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