a: \(=\dfrac{2^{12}\cdot3^{14}}{3^{12}\cdot2^{12}}=3^2=9\)
b: \(=\dfrac{7^3\cdot2\cdot5^3}{5^2\cdot7^2\cdot6}=7\cdot5\cdot\dfrac{1}{3}=\dfrac{35}{3}\)
d: =2^5(2^8+1)/2^2(2^8+1)=2^3=8
c: \(=\dfrac{5^3\cdot3^6\cdot2^8\cdot5^4\cdot3^4\cdot2^2}{2^{10}\cdot3^{10}\cdot5^5}=5^2\)
Bài 1 : Rút gọn
\(M=\dfrac{1^{2016}+2^{2016}+3^{2016}+...+10^{2016}}{2^{2016}+4^{2016}+6^{2016}+...+20^{2016}}\)
Bài 2 : Tính
\(N=\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-9}{89}\)
\(P=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6-8^4.3^5}-\dfrac{5^{10}.7^3-25^5.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
Bài 3: Rút gọn
a) A = |2x + 4,6| - 2x + 15,4
b) B = |x + 7,2| - |x - 1,2|
c) C = 8,5x - 19, 5 - |1,5x + 4,5|
d) D = 8,5 + x - |8,5 - x|
Bài 4 : Tìm x và y \(\in\) N.Biết 25 - y2 = 8(x - 2009)2
Bài 5 ; Cho :
\(A=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{100^2}-1\right)\)
So sánh phân số sau vs \(\dfrac{-1}{2}\)
\(b,\dfrac{x}{2}-\left(\dfrac{3x}{5}-\dfrac{13}{5}\right)=-\left(\dfrac{7}{5}+\dfrac{7}{10}.x\right)\)
\(c,\dfrac{2x-3}{3}+\dfrac{-3}{2}=\dfrac{5-3x}{6}-\dfrac{1}{3}\)
\(d,\dfrac{2}{3x}-\dfrac{3}{12}=\dfrac{4}{5}-\left(\dfrac{7}{x}-2\right)\)
\(e,2\left(x-1\right)=\left(x-1\right)^2\)
a) rút gọn: \(\dfrac{4^5x9^4-2x6^9}{2^{10}x3^8+6^8x20}\)
b) Cho A=\(\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+...\dfrac{99}{2^{99}}+\dfrac{100}{2^{100}}\).So sánh A với 2
Bài 1 : Thực hiện phép tính
a/ \(\dfrac{7}{6}\) - \(\dfrac{13}{12}\) + \(\dfrac{3}{4}\)
b/ 1 \(\dfrac{1}{2}\) . \(\dfrac{-4}{5}\) + \(\dfrac{3}{10}\)
c/ \(\dfrac{25}{9}\) . \(\dfrac{3}{10}\) + ( \(\dfrac{-5}{3}\) )\(^2\) . \(\dfrac{7}{10}\) + | \(\dfrac{-25}{3}\) |
Bài 2 : Tìm x , biết
a/ x - \(\dfrac{5}{6}\) = \(\dfrac{1}{4}\)
b/ \(\dfrac{26}{x}\) = \(\dfrac{-13}{-15}\)
( Cần gấp )
Tính nhanh
\(c,\dfrac{-5}{13}-\left(\dfrac{3}{5}+\dfrac{3}{13}-\dfrac{4}{10}\right)\)
\(d,\left(\dfrac{1}{9}-\dfrac{9}{17}\right)+\dfrac{3}{6}-\left(\dfrac{12}{17}-\dfrac{1}{2}\right)+\dfrac{5}{9}\)
a) \(\dfrac{5}{7}\)+\(\dfrac{3}{4}\).\(\dfrac{-11}{2}\)
b) (\(\dfrac{12}{17}\)+\(\dfrac{19}{7}\)) - (\(\dfrac{-5}{17}\)-\(\dfrac{3}{7}\))
c) (0,125)\(^{12}\).(-8)\(^{12}\)-\(\dfrac{45^3}{15^3}\)
d) \(5\dfrac{2}{7}\).(\(-\dfrac{1}{3}\))-\(2\dfrac{2}{7}\).(\(-\dfrac{1}{3}\))
e) \(\dfrac{9^2.9^3}{3^9}\)
\(d,\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{7}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
a \(\dfrac{-4}{7}\) - \(\dfrac{5}{13}\) x \(\dfrac{-39}{25}\) + \(\dfrac{-1}{42}\) : \(\dfrac{-5}{6}\)
b \(\dfrac{2}{9}\) x [\(\dfrac{4}{45}\): ( \(\dfrac{1}{5}\) - \(\dfrac{2}{15}\)) + 1\(\dfrac{2}{3}\)] - \(\dfrac{-5}{27}\)
