\(\dfrac{75^{50}.2^{100}}{100^{50}.9^{25}}\)
\(=\dfrac{\left(3.5^2\right)^{50}.\left(2^2\right)^{50}}{\left(2^2.5^2\right)+\left(3^2\right)^{50}}\)
\(=\dfrac{ \left(3.25\right)^{50}.4^{50}}{\left(4.25\right)^{50}.3^{50}}\)
\(=\dfrac{3^{50}.25^{50}.4^{50}}{4^{50}.25^{50}.3^{50}}=1\)
\(\left(\dfrac{1}{3}\right)^{50}.\left(-9\right)^{25}-\dfrac{2}{3}:4\)
CMR: \(\dfrac{1}{7^2}-\dfrac{1}{7^4}+...+\dfrac{1}{7^{4n-2}}-\dfrac{1}{7^{4n}}+...+\dfrac{1}{7^{98}}-\dfrac{1}{7^{100}}< \dfrac{1}{50}\)
Chứng minh rằng :
\(\dfrac{1}{7^2} - \dfrac{1}{7^4} + ... + \dfrac{1}{7^{4n-2}} - \dfrac{1}{7^{4n}} + ... + \dfrac{1}{7^{98}}-\dfrac{1}{7^{100}} < \dfrac{1}{50}\)
Tính \(\dfrac{5^{102}.9^{1009}}{3^{2018}.25^{50}}\)
1) \(\left(\dfrac{1}{3}\right)^{50}.90^{25}-\dfrac{2}{3}:4\)
2) \(10.\sqrt{0,01}.\sqrt{\dfrac{16}{9}}+\sqrt{49}-\dfrac{1}{6}.\sqrt{4}\)
1)Thực hiện phép tính
a) \(\dfrac{9^8\cdot5^6}{3^7\cdot27^3\cdot25^4}\) b) \(\dfrac{5^{20}\cdot6^{18}}{15^{20}\cdot4^{10}}\) c) \(\left(\dfrac{1}{3}\right)^{50}\cdot9^{25}-\left(\dfrac{2}{3}\right)^{100}:\left(\dfrac{8}{27}\right)^{33}\) d) \(\left(\dfrac{3}{8}\right)^{60}\cdot\left(\dfrac{2}{3}\right)^{60}:\left(\dfrac{1}{2}\right)^{119}\cdot\left(\dfrac{1}{2}\right)\)
2) Tìm x, biết:
a) \(\dfrac{x}{12}=\dfrac{5}{x}\) b)\(8^x=2^{2x+3}\) c)\(\dfrac{1}{2}\sqrt{\dfrac{1}{2}x-2}-\dfrac{2}{3}=\dfrac{1}{3}\)
\(\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{10}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(\dfrac{\left(1+2+3+...+99+100\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+.....+99-100}\)
Thực hiện phép tính
\(\dfrac{5^{102}.9^{1009}}{3^{2018}.25^{50}}\)
a,\(B=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+......+\dfrac{1}{3^{2004}}+\dfrac{1}{3^{2005}}\)
b,A=\(1+5+5^2+5^3+5^4+.....+5^{49}+5^{50}\)
c,A=\(\left(\dfrac{1}{2^2}-1\right).\left(\dfrac{1}{3^2}-1\right).\left(\dfrac{1}{4^2}-1\right).....\left(\dfrac{1}{100^2}-1\right)\)
d,A=\(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
Ai giúp mình thực hiện phép tính này với ạ?? Cảm ơn nhiều!!
