8⁵=32768

3x4⁷=49152

=>8⁵<3x4⁷

125⁵=30517578125

25⁷=6103515625

=>125⁵>25⁷

Cách ngắn hơn nè:

125^5 và 25^7

Ta có: 125^5= (5^3)^5= 5^15

25^7= (5^2)^7= 5^14

Vì 5^15>5^14 nên 125^5>25^7

8^5=32768<3*4^7=49152

8⁵ = (2³)⁵ = 2¹⁵; 3 x 4⁷ < 4.4⁷ = 4⁸ = (2²)⁸ = 2¹⁶

Vậy  2¹⁵ < 2¹⁶

  8⁵ < 3 x 4⁷

\(A=3\cdot\frac{1}{1\cdot2}-5\cdot\frac{1}{2\cdot3}+7\cdot\frac{1}{3\cdot4}-\cdots+15\cdot\frac{1}{7\cdot8}-17\cdot\frac{1}{8\cdot9}\)

\(=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}-\cdots+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}\)

\(=1+\frac12-\frac12-\frac13+\frac13+\frac14-\cdots+\frac17+\frac18-\frac18-\frac19\)

\(=1-\frac19=\frac89\)

\(\) Ta có:

\(A=\frac{3\cdot1}{1\cdot2}-\frac{5\cdot1}{2\cdot3}+\frac{7\cdot1}{3\cdot4}-\cdots+\frac{15\cdot1}{7\cdot8}-\frac{17\cdot1}{8\cdot9}\)

\(A=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}-\cdots+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}\)

\(A=\frac{1+2}{1\cdot2}-\frac{2+3}{2\cdot3}+\frac{3+4}{3\cdot4}-\cdots+\frac{7+8}{7\cdot8}-\frac{8+9}{8\cdot9}\)

\(A=\left(\frac11+\frac12\right)-\left(\frac12+\frac13\right)+\left(\frac13+\frac14\right)-\cdots+\left(\frac17+\frac18\right)-\left(\frac18+\frac19\right)\)

\(A=\frac11+\frac12-\frac12-\frac13+\frac13+\frac14-\cdots+\frac17+\frac18-\frac18-\frac19\)

\(A=1-\frac19\)

\(A=\frac89\)

Vậy \(A=\frac89\)

\(A=3\cdot\frac{1}{1\cdot2}-5\cdot\frac{1}{2\cdot3}+7\cdot\frac{1}{3\cdot4}-\cdots+15\cdot\frac{1}{7\cdot8}-17\cdot\frac{1}{8\cdot9}\)

\(=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}-\cdots+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}\)

\(=1+\frac12-\frac12-\frac13+\frac13+\frac14-\cdots+\frac17+\frac18-\frac18-\frac19\)

\(=1-\frac19=\frac89\)

áp dụng công thức này là làm được bạn ạ:

\(\frac{a}{b.c}\) =\(\frac{a}{b}-\frac{a}{c}\)

Giải:

A=5/9+2/15-6/9

   =(5/9-6/9)+2/15

   = -1/9 + 2/15

   = 1/45

B=2/7-3/8+4/7+1/7-5/8+5/15

   = (2/7+4/7+1/7) + (-3/8-5/8) +1/3

   = 1+ (-1) +1/3

   =1/3

C=3/5+1/15+1/57+1/3-2/9-3/4-1/36

   =9/15+1/15+1/57+19/57-8/36-27/36-1/36

   =(9/15+1/15)+(1/57+19/57)+(-8/36-27/36-1/36)

   =2/3+20/57+(-1)

   =58/57+(-1)

   =1/57

D=1/1.2+1/2.3+1/3.4+...+1/99.100

   =1/1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100

   =1/1-1/100

   =99/100

Câu E mình ko biết làm nhé!

_ ý bạn la gì

A = ( -4/5 + 4/3 ) + (-5/4 + 14/5) - 7/3

  =   8/15 + 31/20 - 7/3

  =  25/12 - 7/3

  = -1/4

B = 8/3 x 2/5 x 3/8 x 10x 19/92

   = 16/15 x 15/4 x 19/92

   = 4x19/92

   = 19/23

C = - \(\dfrac{5}{7}\) x \(\dfrac{2}{11}\) + \(\dfrac{-5}{7}\) x \(\dfrac{9}{14}\) + \(\dfrac{1}{57}\)

   = - \(\dfrac{10}{77}\) - \(\dfrac{45}{98}\) + \(\dfrac{1}{57}\)

  = - \(\dfrac{635}{1078}\) + \(\dfrac{1}{57}\)

 = - \(\dfrac{36195}{61446}\) + \(\dfrac{1078}{61446}\)

 = - \(\dfrac{35117}{61446}\)

CÁC BN ĐÃ MUA CHƯA

MILK MUA RÙI

1) 2^x . 2² -  2^x  = 3.2⁵

2^x(2² - 1) = 3.2⁵ 

2^x= 2⁵ suy ra x=5

2) a, 3⁵⁰⁰ = 3^5.100 = 243¹⁰⁰

        7³⁰⁰ = 7^3.100 = 343¹⁰⁰  

 ^{Ta thấy 243<343 nên} 7³⁰⁰ > 3⁵⁰⁰

     b, 8⁵ = (2x4)⁵ = 2⁵x4⁵  = 2x 4x4x4⁵ =2x4⁷ < 3x4⁷

Nên 8⁵ < 3x4⁷