(0,8)⁵ : (0,4)⁶

= (4/5)⁵ : (2/5)⁶

= 1024/3125 : 64/15625

= 16 . 5

= 80

\(\left(0,8\right)^5:\left(0,4\right)^6\\ =\left(\dfrac{4}{5}\right)^5:\left(\dfrac{2}{5}\right)^6\\ =\dfrac{1024}{3125}:\dfrac{64}{15625}\\ =16.5\\ =80\)

\(\left(\dfrac{11}{4}\right)^{12}:\left(-\dfrac{11}{4}\right)^{11}\)

\(=\left(-\dfrac{11}{4}\right)^{12}:\left(-\dfrac{11}{4}\right)^{11}\)

\(=\left(-\dfrac{11}{4}\right)^{12-11}\)

\(=\left(-\dfrac{11}{4}\right)^1\)

\(=-\dfrac{11}{4}\)

(11/4)^12:(-11/4)^11

(3/7)² . (-7)⁴

= (3/7)² . 7⁴

= (3/7)² . 7² . 7²

= 9 . 49

= 441

\(\left(\dfrac{3}{7}\right)^2.\left(-7\right)^4\\ =\left(\dfrac{3}{7}\right)^2.7^4\\ =\left(\dfrac{3}{7}\right)^2.7^2.7^2\\ =9.49\\ =441\)

Vì \(\dfrac{1}{11}>\dfrac{1}{18}>\dfrac{1}{21}>\dfrac{1}{24}>\dfrac{1}{27}>\dfrac{1}{29}\)

\(\Rightarrow\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}>\dfrac{1}{4}+\dfrac{1}{11}+\dfrac{1}{18}+\dfrac{1}{21}+\dfrac{1}{24}+\dfrac{1}{27}+\dfrac{1}{29}\)\(\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}+\dfrac{1}{11}=\dfrac{1}{11}.7=\dfrac{7}{11}\)

Ta có:

\(\dfrac{7}{11}=\dfrac{7.5}{11.5}=\dfrac{35}{55};\dfrac{4}{5}=\dfrac{4.11}{5.11}=\dfrac{44}{55}\)

\(Vì\) \(\dfrac{44}{55}>\dfrac{35}{55}\)

\(\Rightarrow\dfrac{4}{5}>\dfrac{7}{11}\)

\(\Rightarrow\dfrac{1}{4}+\dfrac{1}{11}+\dfrac{1}{18}+\dfrac{1}{21}+\dfrac{1}{24}+\dfrac{1}{27}+\dfrac{1}{29}< \dfrac{4}{5}\left(đpcm\right)\)

Ta thấy :

\(\dfrac{1}{4}+\dfrac{1}{11}< \dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1}{2}=1-\dfrac{1}{2}\)

\(\dfrac{1}{18}+\dfrac{1}{21}< \dfrac{1}{12}+\dfrac{1}{12}=\dfrac{1}{6}=\dfrac{1}{2}-\dfrac{1}{3}\)

\(\dfrac{1}{24}+\dfrac{1}{27}< \dfrac{1}{24}+\dfrac{1}{24}=\dfrac{1}{12}=\dfrac{1}{3}-\dfrac{1}{4}\)

\(\dfrac{1}{29}< \dfrac{1}{20}=\dfrac{1}{4}-\dfrac{1}{5}\)

\(\Rightarrow\dfrac{1}{4}+\dfrac{1}{11}+\dfrac{1}{18}+\dfrac{1}{21}+\dfrac{1}{24}+\dfrac{1}{27}+\dfrac{1}{29}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\)

\(\Rightarrow\dfrac{1}{4}+\dfrac{1}{11}+\dfrac{1}{18}+\dfrac{1}{21}+\dfrac{1}{24}+\dfrac{1}{27}+\dfrac{1}{29}< 1-\dfrac{1}{5}=\dfrac{4}{5}\)

\(\Rightarrow dpcm\)

Bài 4

4a, 12,48 x 3,47 - 3,47 x 2,48

= 3,47 x ( 12,48 - 2,48)

= 3,47 x 10

= 34,7

4b, 128 x 68 + 16 x 256

= 128 x 68 + 16 x 2 x 128

= 128 x (68 + 32)

= 128 x 100

 12800

4c, (7,29 + 9,34 + 8,27) - (7,34 + 6,27 + 5,29)

= 7,29 + 9,34 + 8,27 - 7,34 - 6,27 - 5,29

= (7,29 - 5,29) + (9,34 - 7,34) + (8,27 - 6,27)

= 2 + 2 + 2

= 6

2a,

(100 + 67) x 67 + (200 - 33) x 33

= 167 x 67 + 167 x 33

= 167 x (67 + 33)

= 167 x 100

= 16700

2b, 45,651 x 73 + 45,651 x 20 + 45,651 x 7

= 45,651 x (73 + 20 + 7)

= 45,651 x 100

= 4565,1

D = 3\(\dfrac{1}{2}\) \(\times\) \(\dfrac{12}{43}\) + \(\dfrac{49}{14}\) \(\times\) \(\dfrac{31}{43}\) + \(\dfrac{11}{2}\)

D = \(\dfrac{7}{2}\) \(\times\) \(\dfrac{12}{43}\) + \(\dfrac{7}{2}\)  \(\times\) \(\dfrac{31}{43}\) + \(\dfrac{11}{2}\)

D = \(\dfrac{7}{2\times43}\) \(\times\) (12 + 31) + \(\dfrac{11}{2}\)

D = \(\dfrac{7}{2\times43}\)  \(\times\) 43 + \(\dfrac{11}{2}\)

D = \(\dfrac{7}{2}\) + \(\dfrac{11}{2}\)

D = 9

D = 3 và 1/2 x 12/43 + 49/14 x 31/43 + 11/2
= 7/2 x 12/43 + 49/14 x 31/43 + 11/2
= 42/43 +  217/36 + 11/2
=9

# https://lazi.vn/user/tnsociu

1a, 6,28 x 18,24 + 18,24 x 3,72

= 18,24 x (6,28 + 3,72)

= 18,24 x 10

= 182,4

b, 35,7 x 99 + 35 + 0,7

= 35,7 x 99 + 35,7

= 35,7  x (99 + 1)

= 35,7 x 100

= 3570

\(\Rightarrow\) The bigger an apartment is, the higher its rent is

#Wendy Dang

Mik sửa vế 2 nhé :

\(\Rightarrow\) The bigger an apartment is, the higher the rent is

\(111+999=1110\)

\(222+333=555\)

\(406+903=1309\)

\(102+870=972\)

\(784+655=1439\)

\(232+980=1212\)

#Wendy Dang