a,\(\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{999}+1\right)\)

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.....\dfrac{1000}{999}\)

\(=\dfrac{3.4.5....1000}{2.3.4....999}=\dfrac{1000}{2}=500\)

b,\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{1000}-1\right)\)

\(=\dfrac{-1}{2}.\dfrac{-2}{3}.\dfrac{-3}{4}.....\dfrac{-999}{1000}\)

=\(\dfrac{-\left(1.2.3....999\right)}{2.3.4....1000}=\dfrac{-1}{1000}\)

c,\(\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}....\dfrac{99}{10^2}\)

\(=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}....\dfrac{9.11}{10.10}\)

\(=\dfrac{1.3.2.4.3.5....9.11}{2.2.3.3.4.4....10.10}\)

\(=\dfrac{1.2.3...9}{2.3.4...10}.\dfrac{3.4.5...11}{2.3.4...10}\)

\(=\dfrac{1}{10}.\dfrac{11}{2}=\dfrac{11}{20}\)

3⁶ . 4⁶ = (3.4)⁶ = 12⁶

8² . 2³ . 16² = (2³)² . 2³ . (2⁴)

= 2⁶ . 2³ . 2⁴ = 2^{6 + 3 + 4} = 2¹³

2³ . 2² . 8³ = 2³ . 2² . (2³)³

= 2³ . 2² . 2⁹ = 2^{3 + 2 + 9} = 2¹⁴

y. y⁷ = y^{1 + 7} = y⁸

\(3^6\cdot4^6=\left(3\cdot4\right)^6=12^6\)

\(8^2\cdot2^3\cdot16^2=\left(2^3\right)^2\cdot2^3\cdot\left(2^4\right)^2\)

\(=2^6\cdot2^3\cdot2^8=2^{17}\)

\(2^3\cdot2^2\cdot8^3=2^5\cdot\left(2^3\right)^3\)

\(2^5\cdot2^9=2^{14}\)

\(y\cdot y^7=y^{1+7}=y^8\)

3⁶ . 4⁶

= ( 3 . 4 )⁶

= 12⁶

8² . 2³ . 16²

= ( 2³ )² . 2³ . ( 2⁴ )²

= 2⁶ . 2³ . 2⁸

= 2⁶⁺³⁺⁸

= 2¹⁷

2³ . 2² . 8³

= 2³ . 2² . ( 2³ )³

= 2³ 2² . 2⁹

= 2³⁺²⁺⁹

= 2¹⁴

y . y⁷

= y¹ . y⁷

= y¹⁺⁷

= 7⁸

a) \(4^{13}+4^{14}+4^{15}+4^{16}=4^{13}\left(1+4\right)+4^{14}\left(1+4\right)=4^{13}.5+4^{14}.5=5\left(4^{13}+4^{14}\right)⋮5\Rightarrow dpcm\)

c) \(2^{10}+2^{11}+2^{12}+2^{13}+2^{14}+2^{15}\)

\(=2^{10}\left(1+2+2^2\right)+2^{13}\left(1+2+2^2\right)\)

\(=2^{10}.7+2^{13}.7=7\left(2^{10}+2^{13}\right)⋮7\Rightarrow dpcm\)

Câu c bạn xem lại đê

b) ...........

= 1/2x2/3x.....x999/1000

= 1x2x...x999/2x3x...x1000

=1/1000

a) ...............

= 3/2 . 4/3 .... 1000/999

= 3x4x5x....x1000/2x3x4x...x999

=1000/2=500

\(A=4+4^2+...+4^{99}\)

\(\Rightarrow4A=4^2+3^3+...+4^{99}+4^{100}\)

\(\Rightarrow4A-A=4^{100}-4\)

\(\Rightarrow3A=4^{100}-4\Rightarrow A=\frac{4^{100}-4}{3}\)

\(B=5+5^2+...+5^{10}\)

\(5B=5^2+5^3+...+5^{10}+5^{11}\)

\(5B-B=4B=5^{11}-5\Rightarrow B=\frac{5^{11}-5}{4}\)

C đang 6 mũ sao tự nhiên nhảy đâu ra 9 mũ?

Nếu nó là 6 mũ thì làm tương tự như 2 câu trên

Ai đó help me mai lộp rồi

a)64:2mũ5×30×4

= 64 : 32 x 30 x 4

= 240

b)3 mũ 2× 5 - 2 mũ 2×7+2 mũ 0 × 5

= 9 x 5 - 4 x 7 + 1 x 5

= 45 - 28 + 5

= 22

c)2 mũ 3-5 mũ 3÷5 mũ 2 + 12×2 mũ 2

= 8 - 125 : 25 + 12 x 4

= 8 - 5 + 48

= 51

d)2[(7-3 mũ 3÷3 mũ 2) chia 2 mũ 2 + 99]-100

= 2[( 7 - 27 : 9) : 4 + 99] - 100

= 2[4 : 4 + 99] - 100

= 2. 100 - 100

= 200 - 100

= 100

e)4[(3 + 3^7:3^4)chia 10 + 97]-300

= 4[( 3 + 3^3) : 10 + 97] - 300

= 4[ 30 : 10 + 97 ] - 300

= 4. 100 - 300

= 400 - 300

= 100

f)2^2 x 5 [(5 mũ 2 cộng 2 mũ 3) chia 11 - 2] - 3^2 x 2

= 4 x 5 [ (25 + 8 ) : 11 - 2] - 9 x 2

= 20 [ 33 : 11 - 2] - 18

= 20. 1 - 18

= 20 - 18

= 2

hum biết nữa

a)240

b)22

c)51

d)100

e)100

f)2

3. 3³.19-3³.12=3³.(19-12)=3³.7=189

4. 3.5²-16:2²=3.5²-2⁴:2²=3.25-4=75-4=71

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

giải giúp mình bài 2 trên với ạ