a) (2^x)⁵ : 4³ = 8¹⁵ => 2^5x = 8¹⁵.4³ = (2³)¹⁵.(2²)³ = 2⁴⁵.2⁶ = 2⁵¹ => 5x = 51 => x = 10,2 

b) (3²)^x .9³ = 243⁹ => 3^2x = 243⁹ : 9³ = (3⁵)⁹ : (3²)³ = 3⁴⁵ : 3⁶ = 3³⁹ => 2x = 39 => x = 19,5

c) (1/125)³.5^x = 25⁵ => 5^x = 25⁵ : (1/125)³ = (5²)⁵ : (1/5³)³ = 5¹⁰ : (5^-3)³ = 5¹⁰ : 5^-9 = 5¹⁹ => x = 19

d) 1/81 : 3^x = 1/729 => 3^x = 1/81 : 1/729 = 1/3⁴.729 = 3^-4.3⁶ = 3² => x = 2

e) (5x - 2)⁴ = 16⁸ = (16²)⁴ = 256⁴

=> 5x - 2 = -256 ; 256 => 5x = -254 ; 258 => x = -50,8 ; 51,6

P/S : Thay x = 10,2 vào câu a , x = 19,5 vào câu b sẽ thấy điều hư cấu : 2^10,2 và 9^19,5.Ko thể tính được giá trị của 2 lũy thừa này.

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a) 3/7 + 4/9 + 4/7 + 5/9

= ( 3/7 + 4/7 ) + ( 4/9 + 5/9 )

= 7/7 + 9/9

= 1  + 1 

= 2

b)1/5 + 4/10 + 9/15 + 16/20 + 25/25 + 36/30 + 49/35 + 64/40 + 81/45

= 1/5 + 2/5 + 3/5 + 4/5 + 5/5 + 6/5 + 7/5 + 8/5 + 9/5

= ( 1/5 + 9/5 ) + ( 2/5 + 8/5 ) + (7/5 + 3/5 ) + ( 4/5 + 6/5  ) + 5/5

= 2 + 2 + 2 + 2 + 1

= 2  x 4 + 1

= 8  +1 

= 9

c)  1/8 + 1/12 + 3/8 + 5/12

= ( 1/8 + 3/8 ) + ( 1/12 + 5/12)

= 4/8 + 6/12

= 1/2 + 1/2

= 2/4 = 1/2

mỏi tay rồi

1) Ta có: \(\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{7}{25}\cdot\dfrac{5}{7}\right)\)

\(=\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{1}{5}\right)\)

=0

2) Ta có: \(\dfrac{8}{17}\cdot\dfrac{4}{15}+\dfrac{8}{17}\cdot\dfrac{22}{15}-\dfrac{8}{15}\cdot\dfrac{9}{17}\)

\(=\dfrac{8}{17}\left(\dfrac{4}{15}+\dfrac{22}{15}-\dfrac{9}{15}\right)\)

\(=\dfrac{8}{17}\cdot\dfrac{15}{15}=\dfrac{8}{17}\)

3) Ta có: \(\dfrac{2021}{2}\cdot\dfrac{1}{3}+\dfrac{4042}{4}\cdot\dfrac{1}{5}+\dfrac{6063}{3}\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)+2021\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{8}{15}+\dfrac{2021}{2}\cdot\dfrac{44}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{52}{15}\)

\(=\dfrac{52546}{15}\)

4) Ta có: \(\dfrac{4}{7}\cdot\dfrac{2}{13}+\dfrac{8}{13}:\dfrac{7}{4}+\dfrac{4}{7}:\dfrac{13}{2}+\dfrac{4}{7}\cdot\dfrac{1}{13}\)

\(=\dfrac{4}{7}\left(\dfrac{2}{13}+\dfrac{8}{13}+\dfrac{2}{13}+\dfrac{1}{13}\right)\)

\(=\dfrac{4}{7}\)

1) Tính biểu thức:

\(a,121-\left(115+x\right)=3x-\left(25-9-5x\right)-8\\ 121-115-x=3x-25+9+5x-8\\ 6-x=8x-24\\ 8x+x=-24-6\\ 9x=-30\\ x=-\dfrac{30}{9}=-\dfrac{10}{3}\\ ----\\ b,2^{x+2}.3^{x+1}.5^x=10800\\ \left(2.3.5\right)^x.2^2.3=10800\\ 30^x.12=10800\\ 30^x=\dfrac{10800}{12}=900=30^2\\ Vậy:x=2\)

a) 4+2/5=22/5

b) 5/4+2=13/4

c) 3+3/2=9/2

d) 3/4-1/8=5/8

e) 17/15-7/10=13/30

g) 25/12-15/8=5/24

h) 5-4/3=11/3

i)15/4-3=3/4

a)\(\dfrac{4}{1}+\dfrac{2}{5}=\dfrac{20}{5}+\dfrac{2}{5}=\dfrac{22}{5}\)

b)\(\dfrac{5}{4}+\dfrac{2}{1}=\dfrac{5}{4}+\dfrac{8}{4}=\dfrac{13}{4}\)

c)\(\dfrac{3}{1}+\dfrac{3}{2}=\dfrac{6}{2}+\dfrac{3}{2}=\dfrac{9}{2}\)

d)\(\dfrac{3}{4}-\dfrac{1}{8}=\dfrac{6}{8}-\dfrac{1}{8}=\dfrac{5}{8}\)

e)\(\dfrac{17}{15}-\dfrac{7}{10}=\dfrac{34}{30}-\dfrac{21}{30}=\dfrac{13}{30}\)

g)\(\dfrac{25}{12}-\dfrac{15}{8}=\dfrac{50}{24}-\dfrac{45}{24}=\dfrac{5}{24}\)

h)\(\dfrac{5}{1}-\dfrac{4}{3}=\dfrac{15}{3}-\dfrac{4}{3}=\dfrac{11}{3}\)

i)\(\dfrac{15}{4}-\dfrac{3}{1}=\dfrac{15}{4}-\dfrac{12}{4}=\dfrac{3}{4}\)

4/1+2/5= 20/5+2/5= 22/5

5/4+2/1= 5/4+ 8/4= 13/4

3/1+3/2= 6/2+ 3/2= 9/2

6/8- 1/8= 5/8

34/30- 21/30= 13/30

50/24- 45/24= 5/24

5/1- 4/3= 15/3- 4/3= 11/3

15/4- 3/1= 15/4- 12/4= 3/4

a: =5*1,4-4*1,5+3*1,3

=7-6+3,9=4,9

b: =1/3*7+3/4*18-2/3*20

=7/3+54/4-40/3

=-11+54/4

=2,5

c: =5/6*17-1/2*16+2/5*15

=85/6-8+6

=85/6-2

=73/6

d: =15*4/5+12*3/4-18*4/9

=12+9-8

=12+1=13