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

  Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

\(a,\)\(\frac{2^5\times3^{12}\times7^8}{2^7\times3^{10}\times7^9}=\frac{3^2\times\left(2^5\times3^{10}\times7^8\right)}{2^2\times7\times\left(2^5\times3^{10}\times7^8\right)}\)\(=\frac{3^2}{2^2\times7}=\frac{9}{28}\)

\(b,\)Tương tự

7: \(\left(xy+4\right)^2-\left(2x+2y\right)^2\)

=(xy+4-2x-2y)(xy+4+2x+2y)

=[x(y-2)-2(y-2)][x(y+2)+2(y+2)]

=(x-2)(y-2)(x+2)(y+2)

8: \(81x^2-64y^2=\left(9x\right)^2-\left(8y\right)^2\)

=(9x-8y)(9x+8y)

9: \(\left(a^2+b^2+5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2+5\right)^2-\left(2ab+4\right)^2\)

\(=\left(a^2+b^2+5-2ab-4\right)\left(a^2+b^2+5+2ab+4\right)\)

\(=\left\lbrack\left(a-b\right)^2+1\right\rbrack\left\lbrack\left(a+b\right)^2+9\right\rbrack\)

10: \(\left(x-1\right)^2-\left(x+1\right)^2\)

=(x-1-x-1)(x-1+x+1)

=2x*(-2)=-4x

11: \(8x^3-\frac18=\left(2x\right)^3-\left(\frac12\right)^3=\left(2x-\frac12\right)\left(4x^2+2x\cdot\frac12+\frac14\right)\)

\(=\left(2x-\frac12\right)\left(4x^2+x+\frac14\right)\)

12: \(\frac{1}{25}x^2-64y^2=\left(\frac15x\right)^2-\left(8y\right)^2=\left(\frac15x-8y\right)\left(\frac15x+8y\right)\)

13: \(x^3+\frac{1}{27}=x^3+\left(\frac13\right)^3=\left(x+\frac13\right)\left(x^2-\frac13x+\frac19\right)\)

\(2+2^2+2^3+...+2^{11}+2^{12}\)

\(=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+\left(2^7+2^8+2^9\right)+\left(2^{10}+2^{11}+2^{12}\right)\)

\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+2^7\left(1+2+2^2\right)+2^{10}\left(1+2+2^2\right)\)

\(=7\left(2+2^4+2^7+2^{10}\right)\)chia hết cho \(7\).

bạn có thể giảng cho mình được ko,chép thì chưa hiểu bài

d, D = 40² - 28² + 32² +80.32

    D = (40² + 2.40.32 + 32²) - 28²

    D = (40 + 32)² - 28²

    D = (40 + 32 - 28)(40 + 32 + 28)

    D = 44.100

   D = 4400

  e, E = 10.80,5 + 10.19,5 - 8.20,5 - 8. 79,5

      E =  10.(80,5 + 19,5) - 8.( 20,5 + 79,5)

      E = 10.100 - 8.100

     E = 100.(10-8)

     E = 200

F = 50² - 18² + 32² + 100.32

F = (50² - 18²) + 32.( 32 + 100)

F = (50 -18)(50+18) + 32. 132

F = 32.68 + 32.132

F = 32.( 68 + 132)

F = 32. 200

F = 6400

a)

\(\text{( 25 – 2x )³ : 5 – 3^2 = 4^2}\)

\(\text{( 25 – 2x )³ : 5 – 9 = 16}\)

\(\text{( 25 – 2x )³ : 5 = 16 + 9}\)

\(\text{( 25 – 2x )³ : 5 = 25}\)

\(\text{( 25 – 2x )³ = 25 . 5}\)

\(\text{( 25 – 2x )³ = 125}\)

\(\text{( 25 – 2x )³ = 5³}\)

\(\text{25 – 2x = 5}\)

\(\text{2x = 25 – 5}\)

\(\text{2x = 20}\)

\(\text{x = 10}\)

\(\text{________________________________________}\)

b)

\(\text{2.3^x = 10.3^12 + 8.27^4}\)

\(\text{2.3^x = 10.3^12 + 8.(3^3)^4}\)

\(\text{2.3^x = 3^12 . (10+8)}\)

\(\text{2.3^x = 3^12 . 18}\)

\(\text{3^x = 3^12 . 18:2}\)

\(\text{3^x = 3^12 . 9}\)

\(\text{3^x = 3^12 . 3^2}\)

\(\text{3^x = 3^14}\)

\(\text{=> x=14}\)