3. 

\(C=5+5^2+...+5^6\\ C=5\left(1+5\right)+5^3\left(1+5\right)+5^5\left(1+5\right)\\ C=5\cdot6+5^3\cdot6+5^5\cdot6\\ C=6\left(5+5^3+5^5\right)\\ =>C⋮6\)

\(4.D=3+3^2+...+3^6\\D=3\left(1+3\right)+3^3\left(1+3\right)+3^5\left(1+3\right)\\ D=3\cdot4+3^3\cdot4+3^5\cdot5\\ C=4\left(3+3^3+3^5\right)\\ =>D⋮4\\ 5.E=4+4^2+...+4^6\\ E=4\left(1+4\right)+4^3\left(1+4\right)+4^5\left(1+4\right)\\ E=4\cdot5+4^3\cdot5+4^5\cdot5\\ E=5\left(4+4^3+4^5\right)=>E⋮5 \)

16) -9/13 . 5/17 + (-17/13) . 5/17

= (-9/13 - 17/13) . 5/17

= -2 . 5/17

= -10/17

17) 7/15 . (-4/9) + (-5/9) . 7/15

= 7/15 . (-4/9 - 5/9)

= 7/15 . (-1)

= -7/15

18) 3/8 . (-23/14) - 3/8 . (-9/14)

= 3/8 . (-23/14 + 9 /14)

= 3/8 . ( -1)

= -3/8

13) -2/3 . 3/11 + (-16/9) . 3/11

= 3/11 . (-2/3 - 16/9)

= 3/11 . (-22/9)

= -2/3

14) -5/9 . 3/11 + (-13/18) . 3/11

= 3/11 . (-5/9 - 13/18)

= 3/11 . (-23/9)

= -23/33

15) 2/13 . (-5/3) + 11/13 . (-5/3)

= -5/3 . ( 2/13 + 11/13)

= -5/3 . 1

= -5/3 

10) 7/15 . 16/13 + 7/15 . (- 3/13)

= 7/15 . (16/13 - 3/13)

= 7/15 . 1

= 7/15

11) -23/7 . 3/10 + 13/7 . 3/10

= 3/10 . (-23/7 + 13/7)

= 3/10 . (- 10/7)

= -3/7

12) -11/8 . 19/3 + 19/3 . -5/8

= 19/3 . ( -11/8 - 5/8)

= 19/3 . (-2)

= -38/3

7) 2/7 . 8/19 + 5/7 . 8/19

= 8/19 . ( 2/7 + 5/7)

= 8/19 . 1

= 8/19

8) 23/15 . 3/8 - 17/15 . 3/8

= 3/8 . ( 23/15 - 17/15)

 = 3/8 . 2/5

= 3/20

9) 3/2 . 5/3 - 7/6 . 3/2

= 3/2 . (5/3 - 7/6) 

= 3/2 . 1/2

= 3/4

4) 7/2 . 11/6 - 7/2 . 5/6

= 7/2 . (11/6 - 5/6)

= 7/2 . 1

= 7/2

5) 11/9 . 3/4 - 2/9 . 3/4

= 3/4 . (11/9 - 2/9)

= 3/4 . 1

= 3/4

6) 3/7 . 13/5 + 3/7 . 8/5

= 3/7 . (13/5 + 8/5)

= 3/7 . 21/5

= 9/5

1) 2/5 . 3/8 + 5/8 . 2/5

= 2/5 . ( 3/8+5/8)

= 2/5 . 1

= 2/5

2) 2/3 . 5/2 - 3/4 . 2/3

= 2/3 . (5/2-3/4)

= 2/3 . (10/4-3/4)

= 2/3 . 7/4

= 7/6

3) 5/7 . 19/23 - 12/23 . 5/7

= 5/7 . (19/23 - 12/23)

= 5/7 . 7/23

= 5/23

3)

\(\left(-\dfrac{3}{4}\right)3x-1=\dfrac{256}{81}\)

\(-\dfrac{9}{4}\cdot x=\dfrac{337}{81}\)

\(x=\dfrac{337}{81}\cdot-\dfrac{4}{9}\)

\(x=-\dfrac{1348}{729}\)

 \(a.5^{27}=\left(5^3\right)^9=125^9\\ 2^{63}=\left(2^7\right)^9=128^9\)

Vì 128⁹ > 125⁹ => 2⁶³ > 5²⁷

^{\(5^{28}=\left(5^4\right)^7=625^7\\ 2^{63}=\left(2^9\right)^7=512^7\)}

Vì 625⁷ > 512⁷ = > 5²⁸ > 2⁶³

Đã CMR: \(5^{27}< 2^{63}< 5^{28}\)

\(b.A=1+2+2^2+2^3+2^4\\ 2A=2+2^2+2^3+2^4+2^5\\ 2A-A=\left(2+2^2+2^3+2^4+2^5\right)-\left(1+2+2^2+2^3+2^4+\right)\\ A=2^5-1\\ 2^5-1=2^5-1=>A=B\\ c,C=3+3^2+....+3^{100}\\ 3C=3^2+......+3^{101}\\ 3C-C=\left(3^2+...+3^{101}\right)-\left(3+...+3^{100}\right)\\ 2C=3^{101}-3\\ C=\dfrac{3^{101}-3}{2}\\ \dfrac{3^{101}-3}{2}=\dfrac{3^{101}-3}{2}=>C=D\)