\(\dfrac{\text{10^9*81^{10}}}{8^4\cdot25^5\cdot9^{10}}\)
help!!!!
Rút gọn :\(\frac{2\cdot3\cdot5+4\cdot9\cdot25+6\cdot9\cdot35+10\cdot21\cdot40}{2\cdot3\cdot5+4\cdot9\cdot35+6\cdot9\cdot49+10\cdot21\cdot56}\)
rút gọn biểu thức
a) \(\frac{20^5\cdot5^{10}}{\left(4\cdot25\right)^5}\)b)\(\frac{6^3+3\cdot6^2+3^3}{-13}\)c)\(\frac{125^{12}}{5^{13}\cdot25^{11}}\)d)\(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}\cdot2^0\right)\cdot2^3\)
e)\(\frac{81^{11}\cdot3^{17}}{27^{10}\cdot9^{15}}\)
\(\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^3\cdot3\right)+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\) .Tính tổng
\(\dfrac{8^{14}}{4^4.64^5}\)
\(\dfrac{9^{10}.27^7}{81^7.3^{15}}\)
\(\left(\dfrac{3}{10}\right)^4.\left(0,3\right)^5.\left(\dfrac{10}{3}\right)^{10}\)
\(\dfrac{\left(4^3\right)^2.9^4}{6^7.8^2}\)
\(\dfrac{4^8.9^4}{6^6.8^3}\)
\(3^6.\left(\dfrac{1}{3}\right)^6.81^2.\dfrac{1}{27^2}\) TÍNH
\(\dfrac{8^{14}}{4^4.64^5}=\dfrac{\left(2^3\right)^{14}}{\left(2^2\right)^4.\left(2^5\right)^5}=\dfrac{2^{42}}{2^8.2^{25}}=2^{42-\left(8+25\right)}=2^9\)
\(\dfrac{9^{10}.27^7}{81^7.3^{15}}=\dfrac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}=\dfrac{3^{20}.3^{21}}{3^{28}.3^{15}}=\dfrac{3^{20+21}}{3^{28+15}}=\dfrac{3^{41}}{3^{41}.3^2}=\dfrac{1}{3^2}=\dfrac{1}{9}\)
\(A=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
\(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)
\(=\dfrac{2^{12}\cdot3^4\cdot2}{2^{12}\cdot3^5\cdot4}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\cdot9}\)
\(=\dfrac{1}{6}-\dfrac{5\cdot\left(-6\right)}{9}=\dfrac{1}{6}+\dfrac{10}{3}=\dfrac{21}{6}=\dfrac{7}{2}\)
Calculate: \dfrac{1}{10} +\dfrac{2}{10} +\dfrac{3}{10} +\dfrac{4}{10} +\dfrac{5}{10} +\dfrac{6}{10} +\dfrac{7}{10} +\dfrac{8}{10} +\dfrac{9}{10} +\dfrac{55}{10}=101+102+103+104+105+106+107+108+109+1055=
Help me please !
Tính
C=\(\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3^6\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
Sửa đề: \(C=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\right)^6\cdot3^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
\(C=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)
\(=\dfrac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^{12}\cdot3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\left(1+2^3\right)}\)
\(=\dfrac{2}{3\cdot4}-\dfrac{5\cdot\left(-6\right)}{9}\)
\(=\dfrac{2}{12}+\dfrac{30}{9}=\dfrac{1}{6}+\dfrac{10}{3}=\dfrac{1}{6}+\dfrac{20}{6}=\dfrac{21}{6}=\dfrac{7}{2}\)
bài 6: tính :
\(\dfrac{10^9.\left(-81\right)^{10}}{\left(-8\right)^4.25^5.9^{10}}\)
b,\(\dfrac{9^4.\left(-4\right)^5.25^3}{8^3,\left(-27\right)^2.5^7}\)
c,\(\dfrac{3^{186}.\left(-25\right)^{50}}{\left(-15\right)^{100}.27^{29}}\)
a: \(=\dfrac{2^9\cdot5^9\cdot3^{40}}{2^{12}\cdot5^{10}\cdot3^{20}}=\dfrac{3^{20}}{5\cdot2^3}\)
b: \(=\dfrac{-3^8\cdot2^{10}\cdot5^6}{2^9\cdot\left(-1\right)\cdot3^6\cdot5^7}=\dfrac{-2}{5}\cdot3^2=-\dfrac{18}{5}\)
c: \(=\dfrac{3^{186}\cdot5^{100}}{5^{100}\cdot3^{187}}=\dfrac{1}{3}\)
Tính: \(\dfrac{2^{19}\cdot27^3-15\cdot\left(-4\right)^9\cdot9^4}{6^9\cdot2^{10}+\left(-12\right)^{10}}\)
\(=\dfrac{2^{19}\cdot3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot2^{10}\cdot3^9+2^{20}\cdot3^{10}}\)
\(=\dfrac{2^{19}\cdot3^9+3^9\cdot2^{18}\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}\)
\(=\dfrac{2^{18}\cdot3^9\left(2+5\right)}{2^{19}\cdot3^9\cdot\left(1+2\cdot3\right)}=\dfrac{1}{2}\)