\(=\frac{21.273.1333.4161.10101}{91.651.2451.6643.14763}\)

\(=\frac{3.7.13.21.31.43.73.57.91.111}{7.13.21.31.43.57.73.91.111.133}=\frac{3}{133}\)

Tuy nhiên cách làm trên phải có máy tính mới làm đc: 

Có thể sử dụng công thức:

\(x^4+x^2+1=\left(x^2+x+1\right)\left(x^2-x+1\right)\)

Sau đó phân h:

\(2^4+2^2+1=\left(2^2+2+1\right)\left(2^2-2+1\right)=7.3\)

\(4^4+4^2+1=\left(4^2+4+1\right)\left(4^2-4+1\right)=21.13\)

....Tiếp tực làm thì sẽ ra đc kết quả:

\(=\frac{3.7.13.21.31.43.73.57.91.111}{7.13.21.31.43.57.73.91.111.133}=\frac{3}{133}\)

Đặt A = 1 + 2 + 2² + 2³ + 2⁴ + ... + 2¹¹

2A = 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹²

2A - A = (2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹²) - (1 + 2 + 2² + 2³ + 2⁴ + ... + 2¹¹)

A = 2¹² - 1

Ta có: \(2^6\equiv1\left(mod9\right)\)

=> \(2^{12}\equiv1\left(mod9\right)\)

=> \(2^{12}-1⋮9\)

=> \(A⋮9\left(đpcm\right)\)

Đặt A = 1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹ + 2¹⁰ + 2¹¹

A = (1 + 2³) + (2 + 2⁴) + (2² + 2⁵) + (2⁶ + 2⁹) + (2⁷ + 2¹⁰) + (2⁸ + 2¹¹)

A = 9 + 2.(1 + 2³) + 2².(1 + 2³) + 2⁶.(1 + 2³) + 2⁷.(1 + 2³) + 2⁸.(1 + 2³)

A = 9 + 2.9 + 2².9 + 2⁶.9 + 2⁷.9 + 2⁸.9

A = 9 .(1 + 2 + 2² + 2⁶ + 2⁷ + 2⁸) \(⋮9\left(đpcm\right)\)

Xóa nhanh đi ko CTV xóa giờ

Chia chúng nó ra

Câu dễ vậy bạn cần hỏi

`A=(8 2/7-4 2/7)-3 4/9`

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

`=4-3-4/9`

`=1-4/9=5/9`

`B=(10 2/9-6 2/9)+2 3/5`

`=10+2/9-6-2/9+2+3/5`

`=4+2+3/5`

`=6+3/5=33/5`

Bài 2:

`a)5 1/2*3 1/4`

`=11/2*13/4`

`=143/8`

`b)6 1/3:4 2/9`

`=19/3:38/9`

`=19/3*9/38=3/2`

`c)4 3/7*2`

`=31/7*2`

`=62/7`

Bài 1:

\(A=\left(8\dfrac{2}{7}-4\dfrac{2}{7}\right)-3\dfrac{4}{9}\) 

\(A=\left(\dfrac{58}{7}-\dfrac{30}{7}\right)-\dfrac{31}{9}\) 

\(A=4-\dfrac{31}{9}\) 

\(A=\dfrac{5}{9}\) 

\(B=\left(10\dfrac{2}{9}-6\dfrac{2}{9}\right)+2\dfrac{3}{5}\) 

\(B=\left(\dfrac{92}{9}-\dfrac{56}{9}\right)+\dfrac{13}{5}\) 

\(B=4+\dfrac{13}{5}\) 

\(B=\dfrac{33}{5}\)

Bài 2:

a) \(5\dfrac{1}{2}.3\dfrac{1}{4}=\dfrac{11}{2}.\dfrac{13}{4}=\dfrac{11.13}{2.4}=\dfrac{143}{8}\) 

b) \(6\dfrac{1}{3}:4\dfrac{2}{9}=\dfrac{19}{3}:\dfrac{38}{9}=\dfrac{19}{3}.\dfrac{9}{38}=\dfrac{3}{2}\) 

c) \(4\dfrac{3}{7}.2=\dfrac{31}{7}.2=\dfrac{31.2}{7}=\dfrac{62}{7}\)

\(S=1+2+2^2+2^3+...+2^{11}\)

\(=\left(1+2\right)+2^2\left(1+2\right)+...+2^{10}\left(1+2\right)\)

\(=3+3\cdot2^2+3\cdot2^4+3\cdot2^6+3\cdot2^8+3\cdot2^{10}\)

\(=3\left(1+2^2+2^4+2^6+2^8+2^{10}\right)⋮3\)

S= (1+2)+2²(1+2)+2⁴(1+2)+2⁶(1+2)+2⁸(1+2)+2¹⁰(1+2)

S=3(1+2²+2⁴+2⁶+2⁸+2¹⁰)

suy ra S chia hết cho 3

a)\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)

\(=1.6:\frac{9^8.3-9^8.9}{9^8.\left(5+7\right)}\)

\(=6:\frac{9^8.\left(3-9\right)}{9^8.12}\)

\(=6:\frac{9^8.\left(-6\right)}{9^8.12}\)

\(=6:\left(-\frac{6}{12}\right)\)

\(=6:\left(-\frac{1}{2}\right)\)

\(=-12\)

b) 3/5 : ( -1/5-1/6)+3/5:(-1/3-16/15) ( mình chuyển về ps luôn )

=3/5: (-11/30) + 3/5 : (-7/5) 

=3/5:[-11/30+(-7/5)]

=3/5:53/30

=18/53

c) (1/2-13/14):5/7-(-2/21+1/7):5/7

= -3/7:5/7-1/21:5/7

=(-3/7-1/21):5/7

=-10/21:5/7

=-2/3

câu b vá c mình làm tắt nha. chúc bạn học tốt

a, = (58/9 + 7/11) - (40/9 - 26/11)

= 701/99 - 206/99

= 5

b, = 51/5 - 11/2 . 60/11 + 3 : 3/20

= 51/5 - 30 + 20

= -99/5 + 20

= 1/5

c, = 19/4 + (-0,37) + 1/8 + (-1,8) + (-2,5) + 37/12

= 219/50 + -67/40 + 7/12

= 1973/600