\(\left(\dfrac{1}{17}\right)^{14}=\dfrac{1}{17^{14}}< \dfrac{1}{16^{14}}=\dfrac{1}{\left(2^4\right)^{14}}=\dfrac{1}{2^{56}}\)
\(\left(\dfrac{1}{31}\right)^{11}=\dfrac{1}{31^{11}}>\dfrac{1}{32^{11}}=\dfrac{1}{\left(2^5\right)^{11}}=\dfrac{1}{2^{55}}\)
1, Tính
a, 2008 . 2008 - 2010 . 2006
b, \(\dfrac{232323.29}{23.292929}\)
c, \(\dfrac{\left(2^{17}+5^{17}\right).\left(3^{14}-5^{12}\right).\left(2^4-4^2\right)}{15^2+5^3+67^7}\)
2, So sánh \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{100}}\) với 1
\(5\dfrac{8}{17}:x+\left(\dfrac{-4}{17}\right):x+3\dfrac{1}{7}:17\dfrac{1}{3}=\dfrac{4}{11}\)
1. Thực hiện phép tính
a. \(25\%-\dfrac{5}{4}+1\dfrac{5}{6}\)
b. \(75\%:2\dfrac{1}{5}-\left(0,5\right)^2.\left(-7\right)+2.5\left(7\dfrac{2}{3}-5\dfrac{2}{3}\right)\)
c. \(45:2\dfrac{4}{7}+50\%-1,25\)
d. \(350\%:\dfrac{105}{24}+4\dfrac{5}{6}:2-\left(0,5\right)^2.30\%\)
e. \(4\dfrac{2}{5}.0.5-1\dfrac{3}{7}.14\%+\left(-0,8\right)\)
f. \(2\dfrac{3}{4}.\left(-0,4\right)-1\dfrac{3}{5}.2,75+\left(-1,2\right);\dfrac{4}{11}\)
tính M = \(\dfrac{1,6:\left(1\dfrac{3}{5}.1,25\right)}{0,64-\dfrac{1}{25}}+\dfrac{\left(1,08-\dfrac{2}{25}\right):\dfrac{4}{7}}{\left(5\dfrac{5}{9}-2\dfrac{1}{4}\right).2\dfrac{2}{17}}+0,6.0,5:\dfrac{2}{5}\)
Tính giá trị biểu thức
a, \(\dfrac{5.8-5.6}{10}\) b, \(\dfrac{\left(-4\right)^2}{5}\) B = \(\dfrac{3}{7}+\left(\dfrac{-1}{5}+\dfrac{-3}{7}\right)\) C = \(\left(6-2\dfrac{4}{5}\right).3\dfrac{1}{8}-1\dfrac{3}{5}:\dfrac{1}{4}\)
D = \(\left(\dfrac{-5}{24}+0,75+\dfrac{7}{12}\right):\left(-2\dfrac{1}{8}\right)\) E = \(\dfrac{-5}{7}.\dfrac{2}{11}+\dfrac{-5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\) F = \(\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2\right)^2\)
Tính
a, 4\(\times\left(-\dfrac{1}{2}\right)^3-2\times\left(-\dfrac{1}{2}\right)^2+3\times\left(-\dfrac{1}{2}\right)+1\)
b, \(\dfrac{4^6\times9^5+6^9\times120}{-8^4\times3^{12}+6^{11}}\)
c, \(\dfrac{155-\dfrac{10}{7}-\dfrac{5}{11}+\dfrac{5}{23}}{403-\dfrac{26}{7}-\dfrac{13}{11}+\dfrac{12}{23}}+\dfrac{\dfrac{3}{5}+\dfrac{3}{13}-0,9}{\dfrac{7}{91}+0,2-\dfrac{3}{10}}\)
d,\(\dfrac{30\times4^7\times3^{29}-5\times14^5\times2^{12}}{54\times6^{14}\times9^7-12\times8^5\times7^5}\)
Tính :
a) \(1\dfrac{13}{15}.\left(0,5\right)^2.3+\left(\dfrac{8}{15}-1\dfrac{19}{60}\right):1\dfrac{23}{24}\)
b) \(\dfrac{\left(\dfrac{11^2}{200}+0,415\right):0,01}{\dfrac{1}{12}-37,25+3\dfrac{1}{6}}\)
Tìm tập hợp các số nguyên m biết:
\(2017^0\)-11≤3m≤\(\left(\dfrac{2016}{2017}-\dfrac{2017}{2018}\right).\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right).\left(-3^2+9\right)\)
a, \(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{2^2}\right)\left(1+\dfrac{1}{2^3}\right)\left(1+\dfrac{1}{2^4}\right)....\left(1+\dfrac{1}{2^{50}}\right)< 3\)
b, \(\dfrac{1}{2}-\dfrac{1}{2^2}+.........+\dfrac{1}{2^{99}}-\dfrac{1}{2^{100}}< \dfrac{1}{3}\)
