a: =35/17-18/17-9/5+4/5

=1-1=0

b: =-7/19(3/17+8/11-1)

=7/19*18/187=126/3553

c: =26/15-11/15-17/3-6/13

=1-6/13-17/3

=7/13-17/3=-200/39

9063/308

\(S=\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}\)

\(S=\frac{4-1}{1\cdot4}+\frac{7-4}{4\cdot7}+\frac{11-7}{7\cdot11}+\frac{14-11}{11\cdot14}+\frac{17-14}{14\cdot17}\)

\(S=\frac{4}{1\cdot4}-\frac{1}{1\cdot4}+\frac{7}{7\cdot4}-\frac{4}{4\cdot7}+\frac{11}{7\cdot11}-\frac{7}{7\cdot11}+\frac{14}{11\cdot14}-\frac{11}{11\cdot14}+\frac{17}{14\cdot17}-\frac{14}{14\cdot17}\)

\(S=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)

\(S=\frac{1}{1}-\frac{1}{17}=\frac{17}{17}-\frac{1}{17}=\frac{16}{17}\)

b: \(27D=3^{14}+3^{17}+...+3^{2024}\)

\(\Leftrightarrow26D=3^{2024}-3^{11}\)

hay \(D=\dfrac{3^{2024}-3^{11}}{26}\)

c: \(25E=-5^4-5^6-...-5^{1002}\)

\(\Leftrightarrow24E=-5^{1002}+5^2\)

hay \(E=\dfrac{-5^{1002}+5^2}{24}\)

sai nha

a) \(\dfrac{\dfrac{3}{14}-\dfrac{3}{17}+\dfrac{3}{19}}{\dfrac{5}{19}+\dfrac{5}{14}-\dfrac{5}{17}}=\dfrac{3\left(\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{19}\right)}{5\left(\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{19}\right)}=\dfrac{3}{5}\)

c) \(\dfrac{\dfrac{2}{7}+\dfrac{2}{5}+\dfrac{2}{17}-\dfrac{2}{193}}{\dfrac{3}{7}+\dfrac{3}{5}+\dfrac{3}{17}-\dfrac{3}{293}}=\dfrac{2\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{193}\right)}{3\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{193}\right)}=\dfrac{2}{3}\)

d) 

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

1) \(\left(+15\right)+\left(+17\right)=15+17=32\)

2) \(\left(-3\right)+\left(-7\right)=-3-7=-\left(3+7\right)=-10\)

3) \(\left(-25\right)+\left(+4\right)=-25+4=-\left(25-4\right)=-21\)

4) \(\left(-6\right)+\left(-54\right)=-6-54=-\left(6+54\right)=-60\)

5) \(\left(-15\right)+20=20-15=5\)

6) \(\left(-5\right)+8+7+5\)

\(=\left(-5+5\right)+\left(8+7\right)\)

\(=15\)

7) \(\left(-8\right)+\left(-11\right)+\left(-2\right)\)

\(=\left[\left(-8\right)+\left(-2\right)\right]+\left(-11\right)\)

\(=\left(-10\right)+\left(-11\right)\)

\(=-21\)

8) \(15+\left(-5\right)+\left(-14\right)+\left(-16\right)\)

\(=\left[15+\left(-5\right)\right]+\left[\left(-14\right)+\left(-16\right)\right]\)

\(=10+\left(-30\right)\)

\(=-20\)

9) \(\left(-20\right)+\left(-14\right)+3+\left(-86\right)\)

\(=\left[\left(-20\right)+3\right]+\left[\left(-14\right)+\left(-86\right)\right]\)

\(=\left(-17\right)+\left(-100\right)\)

\(=-117\)

10) \(\left(-136\right)+123+\left(-264\right)+\left(-83\right)+240\)

\(=\left[\left(-136\right)+\left(-264\right)\right]+\left[123+\left(-83\right)\right]+240\)

\(=\left(-400\right)+40+240\)

\(=\left(-360\right)+240\)

\(=-120\)

11) \(\left(-596\right)+2001+1999+\left(-404+189\right)\)

\(=\left(-596\right)+2001+1999-404+189\)

\(=\left[\left(-596\right)-404\right]+\left(2001+189\right)+1999\)

\(=\left(-1000\right)+2190+1999\)

\(=1190+1999\)

\(=3189\)

12) \(314+\left(-153\right)+64+121+\left(-247\right)+218\)

\(=\left(314+64+121\right)+\left[\left(-153\right)+\left(-247\right)\right]+218\)

\(=\left(378+121\right)+\left(-400\right)+218\)

\(=499-400+218\)

\(=99+218\)

\(=317\)

\(\text{#}Toru\)

có đúng ko

a)\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{-3}{5}.\dfrac{2}{7}+\dfrac{-3}{5}\) 

=\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-2}{5}+\dfrac{-3}{5}\)

=\(-\dfrac{2}{5}.\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{-3}{5}\) 

=\(\dfrac{-2}{5}.1+\dfrac{-3}{5}\) 

=\(-\dfrac{2}{5}+\dfrac{-3}{5}\) 

=\(-\dfrac{5}{5}\) = -1

\(\dfrac{5}{9}.\dfrac{14}{17}+\dfrac{1}{17}.\dfrac{5}{9}+\dfrac{2}{9}+\dfrac{5}{12}\)

=\(\dfrac{5}{9}.\left(\dfrac{14}{17}+\dfrac{1}{17}\right)+\dfrac{2}{9}+\dfrac{5}{12}\) 

=\(\dfrac{5}{9}.\dfrac{15}{17}+\dfrac{2}{9}+\dfrac{5}{12}\) 

=\(\dfrac{25}{51}+\dfrac{2}{9}+\dfrac{5}{12}\)

=\(\dfrac{691}{612}\)