Đề là tính hay tính nhanh vậy cậu?
 

cong tru da thuc la nhu the nao

??????

2/3 x 4/5 + 4/5 x 8/3 = 4/5 x (2/3 + 8/3) = 4/5 x 10/3 = 8/3

27/32 x 16/9 -27/32 x7/9 + 27/32 

= 27/32 x (16/9 - 7/9 + 1 )

=27/32 x 2 

=27/16

\(\frac{2}{3}\) x   \(\frac{4}{5}\) +    \(\frac{4}{5}\) x     \(\frac{8}{3}\)

=\(\frac{4}{5}\) x    ( \(\frac{2}{3}\) +    \(\frac{8}{3}\) )

= \(\frac{4}{5}\) x    \(\frac{10}{3}\)

= \(\frac{40}{15}\) = \(\frac{8}{5}\)

2/9 + 6/27 + 8/36 + 12/54 + 16/72 + 18/81=\(\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}\)  = \(\frac{2}{9}\). 6 = \(\frac{12}{9}\)= \(\frac{4}{3}\)

\(\frac{2}{9}+\frac{6}{27}+\frac{8}{36}+\frac{12}{54}+\frac{16}{72}+\frac{18}{81}\)

\(=\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}\)

\(=\frac{2}{9}×6=\frac{4}{3}\)

a) 1/2 + 3/4 - (3/4 - 4 - 5)

= 1/2 + 3/4 - 3/4 + 4 + 5

= (3/4 - 3/4) + (4 + 5) + 1/2

= 0 + 9 + 1/2

= 19/2

b) [9/16 + 8/(-27)] - (19/27- 7/16 - 2)

= 9/16 - 8/27 - 19/27 + 7/16 + 2

= (9/16 + 7/16) + (-8/27 - 19/27) + 2

= 1 - 1 + 2

= 2

c) -5/8 . [4/9 + 7/(-12)]

= -5/8 . (-5/36)

= 25/288

d) 7/10 . (-3/5) + 7/10 . (-2/5) - (-3/10)

= 7/10 . (-3/5 - 2/5) + 3/10

= 7/10 . (-1) + 3/10

= -2/5

e) -3/7 . 5/9 + 4/9 . (-3/7) + 2 3/7

= -3/7 . (5/9 + 4/9) + 17/7

= -3/7 . 1 + 17/7

= 2

f) 8 2/7 - (3 4/9 + 4 2/7)

= 8 + 2/7 - 3 - 4/9 - 4 - 2/7

= (8 - 3 - 4) + (2/7 - 2/7) - 4/9

= 1 - 4/9

= 5/9

h) 3.(-1/2)² - (4/5 + 8/15) : 5/6

= 3.1/4 - 4/3 : 5/6

= 3/4 - 8/5

= -17/20

DAI QUA . 

😵

           A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)

     2 \(\times\) A = 1   + \(\dfrac{1}{2}\) +  \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\)

 2 \(\times\) A - A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - (\(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\))

        A      = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) - \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) - \(\dfrac{1}{16}\) - \(\dfrac{1}{32}\)

        A       =  1 - \(\dfrac{1}{32}\)

        A       =   \(\dfrac{31}{32}\)

      B = \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\) + \(\dfrac{1}{729}\)

3 \(\times\)B =  1 + \(\dfrac{1}{3}\) +   \(\dfrac{1}{9}\) +  \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\)

3 \(\times\) B - B = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\) -(\(\dfrac{1}{3}\)+\(\dfrac{1}{9}\)+\(\dfrac{1}{27}\)+...+\(\dfrac{1}{729}\))

2B          = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\) + \(\dfrac{1}{243}\) - \(\dfrac{1}{3}\) - \(\dfrac{1}{9}\)-\(\dfrac{1}{27}\)-...- \(\dfrac{1}{729}\)

2B          = 1 - \(\dfrac{1}{729}\)

2B         = \(\dfrac{728}{729}\)

   B = \(\dfrac{728}{729}\) : 2

   B  = \(\dfrac{364}{729}\)

a)

Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:

2/9+6/27+8/36+12/54+16/72+18/81=

2/9+2/9+2/9+2/9+2/9+2/9=

2/9*6=

12/9=

4/3

Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3

b)

Ta có:

1-2/5=3/5

1-2/7=5/7

1-2/9=7/9

...

1-2/99=97/99

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=

3/5*5/7*7/9*...*97/99=

(3*5*7*...*97)/(5*7*9*...*99)=

3/99=

1/33

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33

c)

Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:

S=1/2+1/4+1/8+1/16+...+1/1024

S*2=1+1/2+1/4+1/8+...+1/512

S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)

S=1-1/1024

S=1023/1024

Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024

Cảm ơn bạn nhé!

7)

53.(51+4)+53.(49+96)+53

=53.55+53.145+53

=53.(55+145+1)

=53.201

=10653

8)

42.(15+96)+6.(25+4).7

=42.111+(6.7).29

=42.111+42.29

=42.(111+29)

=42.140

=5880

9)

45.(13+78)+9.(87+22).5

=45.91+(9.5).109

=45.91+45.109

=45.(91+109)

=45.200

=9000

10)

16.(27+75)+8.(53+25).2

=16.102+(8.2).78

=16.102+16.78

=16.(102+78)

=16.180

=2880

7)

53.(51+4)+53.(49+96)+53

=53.55+53.145+53

=53.(55+145+1)

=53.201

=10653

8)

42.(15+96)+6.(25+4).7

=42.111+(6.7).29

=42.111+42.29

=42.(111+29)

=42.140

=5880

9)

45.(13+78)+9.(87+22).5

=45.91+(9.5).109

=45.91+45.109

=45.(91+109)

=45.200

=9000

10)

16.(27+75)+8.(53+25).2

=16.102+(8.2).78

=16.102+16.78

=16.(102+78)

=16.180

=2880

P/s : mk làm từng phần một

\(\left(\frac{2}{3}\right)^x=\frac{8}{27}=\left(\frac{2}{3}\right)^3\)

=> x = 3

Vậy,........

2)

\(\left(\frac{5}{6}x+\frac{1}{2}\right)^2=\frac{9}{16}=\left(\frac{3}{4}\right)^2\)

\(\frac{5}{6}x+\frac{1}{2}=\frac{3}{4}\)

\(\frac{5}{6}x=\frac{1}{4}\)

\(x=\frac{3}{10}\)

3)

\(\left(\frac{2}{3}x+\frac{5}{6}\right)^3=\frac{-125}{27}=\left(\frac{-5}{3}\right)^3\)

\(\frac{2}{3}x+\frac{5}{6}=-\frac{5}{3}\)

\(\frac{2}{3}x=\frac{-5}{2}\)

\(x=\frac{-15}{4}\)

= 16 nha 

=16 nha

la:16