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\(7^6+7^5-7^4\)
\(=7^4\cdot7^2+7^5\cdot7-7^4\)
\(=7^4\cdot\left(7^2+7-1\right)\)
\(=7^4\cdot55\)
\(=7^4\cdot5\cdot11⋮11\left(đpcm\right)\)
\(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)\)
\(=7^4.55⋮11\)
\(=>7^6+7^5-7^4⋮11\)
1. Tính:
a. \(\dfrac{\text{−1 }}{\text{4 }}+\dfrac{\text{5 }}{\text{6 }}=\dfrac{-3}{12}+\dfrac{10}{12}=\dfrac{7}{12}\)
b. \(\dfrac{\text{5 }}{\text{12 }}+\dfrac{\text{-7 }}{8}=\dfrac{10}{24}+\dfrac{-21}{24}=\dfrac{-11}{24}\)
c. \(\dfrac{-7}{6}+\dfrac{-3}{10}=\dfrac{-35}{30}+\dfrac{-9}{30}=\dfrac{-44}{30}=\dfrac{-22}{15}\)
d.\(\dfrac{-3}{7}+\dfrac{5}{6}=\dfrac{-18}{42}+\dfrac{35}{42}=\dfrac{17}{42}\)
2. Tính :
a. \(\dfrac{2}{14}-\dfrac{5}{2}=\dfrac{2}{14}-\dfrac{35}{14}=\dfrac{-33}{14}\)
b.\(\dfrac{-13}{12}-\dfrac{5}{18}=\dfrac{-39}{36}-\dfrac{10}{36}=\dfrac{49}{36}\)
c.\(\dfrac{-2}{5}-\dfrac{-3}{11}=\dfrac{-2}{5}+\dfrac{3}{11}=\dfrac{-22}{55}+\dfrac{15}{55}=\dfrac{-7}{55}\)
d. \(0,6--1\dfrac{2}{3}=\dfrac{6}{10}--\dfrac{5}{3}=\dfrac{3}{5}+\dfrac{5}{3}=\dfrac{9}{15}+\dfrac{25}{15}=\dfrac{34}{15}\)
3. Tính :
a.\(\dfrac{-1}{39}+\dfrac{-1}{52}=\dfrac{-4}{156}+\dfrac{-3}{156}=\dfrac{-7}{156}\)
b.\(\dfrac{-6}{9}-\dfrac{12}{16}=\dfrac{2}{3}-\dfrac{3}{4}=\dfrac{8}{12}-\dfrac{9}{12}=\dfrac{-17}{12}\)
c. \(\dfrac{-3}{7}-\dfrac{-2}{11}=\dfrac{-3}{7}+\dfrac{2}{11}=\dfrac{-33}{77}+\dfrac{14}{77}=\dfrac{-19}{77}\)
d.\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(=\dfrac{1}{1}+\dfrac{1}{10}\)
\(=\dfrac{10}{10}-\dfrac{1}{10}\)
= \(\dfrac{9}{10}\)
Chế Kazuto Kirikaya thử tham khảo thử đi !!!
Mấy câu trên kia dễ rồi mình chữa mình câu \(c\) bài \(3\) thôi nhé Kazuto Kirikaya
d) \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}\)
\(=\dfrac{9}{10}\)
a.\(\dfrac{17}{15}\div\dfrac{4}{3}=\dfrac{17}{20}\)
b.\(\dfrac{-12}{21}\div\dfrac{34}{43}=\dfrac{-86}{119}\)
c.\(\dfrac{-5}{9}\times\dfrac{3}{11}+\dfrac{13}{18}\times\dfrac{3}{11}\)
=\(\dfrac{3}{11}\times(\dfrac{-5}{9}+\dfrac{13}{18})=\dfrac{3}{11}\times\dfrac{1}{6}=\dfrac{1}{22}\)
d.\(\dfrac{-2}{9}\times\dfrac{5}{11}+\dfrac{-16}{9}\times\dfrac{5}{11}=\dfrac{5}{11}\times(\dfrac{-2}{9}+\dfrac{-16}{9})\)
=\(\dfrac{5}{11}\times(-2)=\dfrac{-10}{11}\)
7245 - 7244 = 7244(72-1)=7244.71
7244 - 7243 = 7243(72-1)=7243.71
7245- 7244 > 7244 - 7243
Bài 1:
a) Đề ko rõ, coi lại
b) \(75^{20}=45^{10}.5^{30}\)
\(\Leftrightarrow\left(75^2\right)^{10}=45^{10}.\left(5^3\right)^{10}\)
\(\Leftrightarrow5625^{10}=45^{10}.125^{10}\)
\(\Leftrightarrow5625^{10}=\left(45.125\right)^{10}\)
\(\Leftrightarrow5625^{10}=5625^{10}\)
\(\Rightarrow75^{20}=45^{10}.5^{30}\left(đpcm\right)\)
Bài 2:
a) \(\frac{x}{-4}=\frac{-3}{5}\)
\(\Rightarrow x.5=-4.\left(-3\right)\)
\(\Rightarrow x.5=12\)
\(\Rightarrow x=\frac{12}{5}=2,4\)
b) c) d) Làm tương tự câu a. Bn tự lm cho nhớ
e) \(30.5x=4.12\)
\(\Rightarrow150x=48\)
\(\Rightarrow x=\frac{48}{150}=0,32\)
f) g) Làm tương tự câu e. Bn tự lm cho nhớ
a ) \(\left(-\frac{40}{52}.0,32.\frac{17}{20}\right):\frac{64}{75}\)
= \(\left(-\frac{16}{65}.\frac{17}{20}\right):\frac{64}{75}\)
= \(\left(-\frac{68}{325}\right):\frac{64}{75}\)
= \(\frac{-51}{208}\)
b ) \(-\frac{10}{11}.\frac{8}{9}+\frac{7}{18}.\frac{10}{11}\)
= \(\frac{10}{11}.\left(-\frac{8}{9}+\frac{7}{18}\right)\)
= \(\frac{10}{11}.\left(-\frac{1}{2}\right)\)
= \(\frac{-5}{11}\)
c ) \(\frac{45^{10}.5^{20}}{75^{15}}\)
= \(\frac{5^{10}.3^{20}.5^{20}}{5^{30}.3^{15}}\)
= \(\frac{5^{30}.3^{20}}{5^{30}.3^{15}}\)
= 3 5
= 243
d ) ( - 0,125 ) 3 . 80 4
= -80000
a. \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)
\(=\left(\dfrac{11}{24}+\dfrac{13}{24}\right)+\left(\dfrac{-5}{41}-\dfrac{36}{41}\right)+0,5\)
\(=1+\left(-1\right)+0,5\)
\(=0,5\)
b. \(-12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=-12:\left(\dfrac{-1}{12}\right)^2\)
\(=-12:\dfrac{1}{144}\)
\(=-1728\)
c. \(\dfrac{7}{23}.\left[\left(-\dfrac{8}{6}\right)-\dfrac{45}{18}\right]\)
\(=\dfrac{7}{23}.\dfrac{-23}{6}\)
\(=\dfrac{-7}{6}\)
d. \(23\dfrac{1}{4}.\dfrac{7}{5}-13\dfrac{1}{4}:\dfrac{5}{7}\)
\(=23\dfrac{1}{4}.\dfrac{7}{5}-13\dfrac{1}{4}.\dfrac{7}{5}\)
\(=\left(23\dfrac{1}{4}-13\dfrac{1}{4}\right).\dfrac{7}{5}\)
\(=10.\dfrac{7}{5}\)
\(=14\)
e. \(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right).\left(0,8-\dfrac{3}{4}\right)^2\)
\(=\dfrac{17}{12}.\left(\dfrac{1}{20}\right)^2\)
\(=\dfrac{17}{12}.\dfrac{1}{400}=\dfrac{17}{4800}\)