Tính bằng cách hợp lí nhất :
\(\frac{2^3.5^2.7^23^7}{49.5^3.3^6.11}\)
Tính :
\(\frac{2^3.5^2.7^23^7}{49.5^3.3^6.11}\)
\(\frac{2^35^27^23^7}{49.5^3.3^6.11}\)
= \(\frac{2^31^21^21^7}{7.1^3.1^6.11}\)
= \(\frac{8}{77}\)
a ) 2,25 : \(\frac{-6}{25}\)
b) \(\frac{2^3.5^2.7^2.3^7}{49.5^3.3^6.11}\)
a) 2,25 : \(\frac{-6}{25}=\frac{9}{4}\cdot\frac{-25}{6}=\frac{9\cdot\left(-25\right)}{4\cdot6}=\frac{3\cdot3\cdot\left(-25\right)}{4\cdot3\cdot2}=\frac{-75}{8}\)
b) \(\frac{2^3\cdot5^2\cdot7^2\cdot3^7}{49\cdot5^3\cdot3^6\cdot11}=\frac{2^3\cdot5^2\cdot7^2\cdot3^6\cdot3}{7^2\cdot5^2\cdot5\cdot3^6\cdot11}=\frac{2^3\cdot3}{5\cdot11}=\frac{24}{55}\)
Bài 9 : Tính nhanh nếu có thể :
a, \(\dfrac{2^3.5^2.7^2.3^7}{49.5^3.3^6.11}\) b,\(4.\left(\dfrac{-1}{2}\right)^3-2.\left(\dfrac{-1}{2}\right)^2+3.\left(\dfrac{-1}{2}\right)+1\)
a. \(\dfrac{2^3.5^2.7^2.3^7}{49.5^3.3^6.11}\)
= \(\dfrac{2^3.3}{5.11}=\dfrac{24}{55}\)
b. \(4.\left(\dfrac{-1}{2}\right)^3-2.\left(\dfrac{-1}{2}\right)^2+3\left(\dfrac{-1}{2}\right)+1\)
=\(-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{2}\)
= 3\(\left(\dfrac{-1}{2}\right)\)
=\(\dfrac{-3}{2}\)
tính giá trị biểu thức:
d, \((1/4^2).32^2\)
e, \(2^3.5^2.7^2.3^7\over49.5^3.3^6.11\)
f,\(16^5.2^8\over8^5.5^6\)
Tính bằng cách hợp lí
a)\(\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+....+\frac{7}{69.70}\)
b)\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
giúp mik với, mik đag cần gấp.Tks
b)
\(5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
\(5\left(1-\frac{1}{6}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(5\left(1-\frac{1}{31}\right)\)
\(=\frac{150}{31}\)
a)
\(\frac{7}{10}-\frac{7}{11}+...+\frac{7}{69}-\frac{7}{70}\)
\(=\frac{7}{10}-\frac{7}{70}\)
\(=\frac{3}{5}\)
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}\)
Tính tổng trên bằng cách hợp lí
Đặt \(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}\)
\(\Rightarrow A=\frac{5^2}{5}\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}\right)\)
\(\Rightarrow A=5.\left(1-\frac{1}{31}\right)=5.\frac{30}{31}=\frac{150}{31}\)
Tính giá trị của biểu thức sau bằng cách hợp lí nhất
D = \(\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+...+\frac{2011^2}{2010.2012}\)
\(\dfrac{2^4.5^2.7}{2^3.5.7^2.11}\);\(\dfrac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}\)
\(\dfrac{4^2.5.11}{44.20}\);\(\dfrac{13.15.16}{18.65.7};\dfrac{7.2.8.5^2}{14.2.5}\)
\(\dfrac{2^3.3^3.5}{3.2^3.5^3}\)
a) \(\dfrac{2^4\cdot5^2\cdot7}{2^3\cdot5\cdot7^2\cdot11}=\dfrac{2^3\cdot5\cdot10\cdot7}{2^3\cdot5\cdot7\cdot77}=\dfrac{10}{77}\)
\(\dfrac{2^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot2^4\cdot5^3\cdot14}=\dfrac{2^3\cdot3\cdot5^3\cdot7\cdot3^2\cdot8}{3\cdot2^3\cdot2\cdot5^3\cdot14}=\dfrac{7\cdot3^2\cdot8}{2\cdot14}=\dfrac{63\cdot8}{2\cdot14}=18=\dfrac{1386}{77}\)
tính bằng cách hợp lí:
\(\frac{3}{5}+\frac{3}{11}+\frac{-3}{7}+\frac{-2}{97}-\frac{1}{35}-\frac{3}{4}+\frac{-23}{24}\)