Rút gọn:

a) \(\frac{2^{19}\cdot27+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)                                                                c)\(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)

^{b)\(\frac{\left(\frac{2}{5}\right)^7\cdot5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7\cdot5^2+512}\)}

1. Tìm a,b,c biết:

a) a/b = 8/5; b/c =  2/7 và a+b+c= 61

b) ab = 1/2; bc= 2/3; ac = 3/4

c) 3a=2b; 5b = 7c và 3a + 5c - 7b= 60

2. tìm các số nguyên n sao cho:

1) 5^n + 5^n+2 = 650

2) 32^-n .16^n = 1024

3) 3^-1 .3^n+ 5. 3^n-1 = 162

4) 125. 5\(\ge\)5^n\(\ge\)5 . 25

5) (n^54)^2 = n

6) 243\(\ge\)3^n\(\ge\)9.27

7) 2^n+3 . 2^n = 144

8)3<3^n\(\le\)234

9) 8. 16\(\ge\)2^n\(\ge\)4

10) 4^15. 9^15<2^n.3^n< 18^16. 2^16

11) 4^11. 25^11\(\le\)2^n. 5^n\(\le\)20^12. 5^12

12)\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\).\(\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}\)= 2^n

13) 9. 27^n= 3^5

14) (2^3 : 4) . 2^n= 4

15) 3^-2 . 3^4. 3^n = 3^7

16)2^-1. 2^n  +4.2^n=9.2^5

1. Tìm a,b,c biết:

a) a/b = 8/5; b/c = 2/7 và a+b+c= 61

b) ab = 1/2; bc= 2/3; ac = 3/4

c) 3a=2b; 5b = 7c và 3a + 5c - 7b= 60

2. tìm các số nguyên n sao cho:

1) 5^n + 5^n+2 = 650

2) 32^-n .16^n = 1024

3) 3^-1 .3^n+ 5. 3^n-1 = 162

4) 125. 5\(\ge\)5^n\(\ge\)5 . 25

5) (n^54)^2 = n

6) 243\(\ge\)3^n\(\ge\)9.27

7) 2^n+3 . 2^n = 144

8)3<3^n\(\le\)234

9) 8. 16\(\ge\)2^n\(\ge\)4

10) 4^15. 9^15<2^n.3^n< 18^16. 2^16

11) 4^11. 25^11\(\le\)2^n. 5^n\(\le\)20^12. 5^12

12)\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\).\(\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}\)= 2^n

13) 9. 27^n= 3^5

14) (2^3 : 4) . 2^n= 4

15) 3^-2 . 3^4. 3^n = 3^7

16)2^-1. 2^n +4.2^n=9.2^5

B. Tự luận

I: Đại số:

Bài 1: Thực hiện phép tính

1) 11/24 - 5/41 + 13/24 + 0,5 - 36/41

2) -12 : (3/4 - 5/6)^2

3) 7/23. [(-8/6) - 45/18]

4) \(23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}:\frac{5}{7}\)

5) (\(1+\frac{2}{3}-\frac{1}{4}\) ) (\(0,8\:-\frac{3}{4}\) )^2

6) 16\(\frac{2}{7}:\left(\frac{-3}{5}\right)+28\frac{2}{7}:\frac{3}{5}\)

7) \((2^2:\frac{4}{3}-\frac{1}{2}\) ) . 6/5 - 17

8) (1/3)^50 .(-9)^25 -2/3:4

9) 3/5: ( -1/15 - 1/6 )+3/5:( -1/3 - 1\(\frac{1}{15}\) )

10) (-6,5).5,7+5,7.(-3,5)

11) 10.√0,01.√16/9+3√49-1/6√4

12) \(\frac{2⁴.2⁶}{\left(2⁵\right)^2}-\frac{2⁵.15^3}{6^3.10^2}\)

Bài 2. Tìm x, biết

1) x/12 - 5/6 = 1/12

2) 2/3 - 1\(\frac{4}{15}x=\frac{-3}{5}\)

3) -2^3 + 0,5x =1,5

Nhiêu đó thôi mik còn thiếu nhiều lắm

Bài 1:Thực hiện phép tính:

1,\(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)

2,\(-12:(\frac{3}{4}-\frac{5}{6})^2\)

3,\(\frac{7}{23}.[(-\begin{matrix}8\\6\end{matrix})-\frac{45}{18}]\)

4,\(23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}:\frac{5}{7}\)

5,\((1+\frac{2}{3}-\frac{1}{4})(0,8-\frac{3}{4})^2\)

6,\(16\frac{2}{7}:(\frac{-3}{5})+28\frac{2}{7}:\frac{3}{5}\)

7,\((2^2:\frac{4}{3}-\frac{1}{2}).\frac{6}{5}-17\)

8,\((\frac{1}{3})^{50}.\left(-9\right)^{25}-\frac{2}{3}:4\)

9,\(\frac{3}{5}:(\frac{-1}{15}-\frac{1}{6})+\frac{3}{5}:(\frac{-1}{3}-1\frac{1}{15})\)

10,\(\left(-6,5\right).5,7+5,7.\left(-3,5\right)\)

11,\(10.\sqrt{0,01.\frac{16}{9}+3\sqrt{49}-\frac{1}{6}\sqrt{ }4}\)

12,\(\frac{2^4.2^6}{\left(2^5\right)^2}-\frac{2^5.15^3}{6^3.10^2}\)

Thuc hien phep tinh;

a/ \(\frac{5}{15}+\frac{14}{15}-\frac{12}{9}+\frac{2}{7}+\frac{11}{25}\)

b/ \(4.\frac{-1^3}{2}+\frac{1}{2}\)

c/ \(\frac{10^3+5.10^2+5^3}{6^3+3.6^2+3^3}\)

d/ \(\frac{2^8.9^2}{6^4.8^2}\)

e/(\(9\frac{3}{4}:5,2+3,4.2\frac{7}{34}\)):(-1\(\frac{9}{16}\))

f/\(\frac{\frac{2^3}{3}.\frac{-3^2}{4}.\left(-1\right)^5}{\frac{2^2}{5}.\frac{-5^3}{6}}\)