Ta có:\(7^0+7^1+7^2+...+7^{2011}\)

\(=\left(1+7\right)+\left(7^2+7^3\right)+...+\left(7^{2010}+7^{2011}\right)\)

\(=8+8.49+...+8.7^{2010}\)

\(=8\left(1+49+..+7^{2010}\right)⋮8\)

Vậy \(7^0+7^1+7^2+...+7^{2010}+7^{2011}⋮8\)

= 7 mũ ko . 1 + 7 mũ 0 .7 ( tách 7 mũ 1 ) +.........+ 7 mũ 2010 .1 + 7 mũ 2010 . 7

= 7 mũ ko . ( 1+7 ) + 7 mũ 2 . ( 1 + 7 ) + ..... + 7 mũ 2010 . ( 1+ 7 )

= 7 mũ ko . 8 + 7 mũ 2 . 8 + .... + 7 mũ 2010 . 8 

= ( 7 mũ 0 + 7 mũ 2 + 7 mũ 4 + .... + 7 mũ 2008 + 7 mũ 2010 ) . 8 .... chia hết cho 8 

=> ( 7 mũ 0 + 7 mũ 1 + 7 mũ 2 + ..... 7 mũ 2010 + 7 mũ 2011 ) chia hết cho 8

a, (x-35)-120=0

x-35=120+0

x-35=120

x=120+35

x=155

b,7x-8=713

7x=713+8

7x=721

x=721:7

x=103

c,4x:17=0

4x=0.17

4x=0

x=0:4

x=0

d,75+(131-x)=205

131-x=205-75

131-x=130

x=131-130

x=1

e,2x-36=4^6:4^3

2x-36=4^6-3

2x-36=4^3

2x-36=48

2x=48-36

2x=12

x=12:2

x=6

f, 2011^2.2011^x=2011^6

2011^x=2011^6: 2011^2

2011^x=2011^6-2

2011^x=2011^4

x=4

bn

\(\text{a/ ( x-35 ) - 120 = 0}\)

\(\Rightarrow\left(x-35\right)=120\)

\(\Rightarrow x=120+35\)

\(x=155\)

\(\text{b/ 7x - 8 = 713}\)

\(\Rightarrow7x=713+8=721\)

\(x=721:7=103\)

\(\text{c/ 4x : 17 = 0}\)

\(4x=0\)

\(x=0\)

\(\text{d/ 75+(131-x) = 205}\)

\(131-x=205-75=130\)

\(x=131-130=1\)

\(e.2x-36=4^6:4^3\)

\(2x-36=4^3=64\)

\(2x=64+36=100\)

\(x=100:2=50\)

\(f.2011^2.2011^x=2011^6\)

\(\text{Ta có công thức }:x^n.x^m=x^{n+m}\)

\(\Rightarrow x=6-2=4\)

Câu 5: D

Câu 6: A

Câu 4: B

Câu 7: B

Câu 8: C

giải thích câu 8 giúp mik

a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)

 1/2 x 2 mũ n cộng 4 x 2 mũ n = 9 x 2 mũ n

1. 5³ = 5.5.5 = 125

2. 2⁷ = 2.2.2.2.2.2.2 = 128

3. 4⁴ = 4.4.4.4 = 256

4. 7³ = 7.7.7 = 343

6. 3⁵ = 243

7. 2⁶ =  64

8. 3⁴ =  81

9. 8³ =  512

11. 13² = 169

12. 11² = 121

13. 14² = 196

14. 15² = 225

16. 17² = 289

17. 18² = 324

18. 19² = 361

19. 20² = 400

21. 10⁴ = 10000

22. 10⁵ = 100000

23. 10⁶ = 1000000

24. 10⁷ = 10000000

bạn làm như bạn gia hân là đúng nhé

`#3107.101107`

\(3^9\div3^8+5^8\div5^7\\ =3^{9-8}+5^{8-7}\\ =3+5\\ =8\)

_______

\(6^9\div6^7-30\\ =6^{9-7}-30\\ =6^2-30\\ =36-30\\ =6\)

________

\(\left(2^7\times2^2\right)\div2^9-5^0\\ =2^{7+2}\div2^9-1\\ =2^9\div2^9-1\\ =2^0-1\\ =1-1\\ =0\)

_______

\(3\times3\times3\times3\times3\times3^5\\ =3^{1+1+1+1+1+5}\\ =3^{10}\)

3629491209

chu so tan cung la 4 nha ban . Nho k cho minh nhe

bn kiểm tra giúp mk đề 2 câu cuối , mk làm ko ra