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4 tháng 1 2022
\(\dfrac{45^{10}\cdot5^{20}}{75^{15}}=\dfrac{\left(3^2\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{3^{20}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{30}}=3^5=243\\ \dfrac{6^6+6^3+3^3+3^6}{-73}=\dfrac{46656+216+27+729}{-73}=-\dfrac{47628}{73}\\ \dfrac{27^7+3^{15}}{9^9-27}=\dfrac{\left(3^3\right)^7+3^{15}}{\left(3^2\right)^9-3^3}=\dfrac{3^{21}+3^{15}}{3^{18}-3^3}=\dfrac{3^{15}\left(3^6+1\right)}{3^3\left(3^{15}-1\right)}=\dfrac{3^5\cdot730}{3^{15}-1}\\ \dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}=1024\)
6 tháng 10 2022
a: \(=\dfrac{2^{13}\cdot5^7\left(2^{17}+5^{20}\right)}{2^{10}\cdot5^7\left(2^{17}+5^{20}\right)}=2^3\)
b: \(M=\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}\)
\(=3^{2\cdot1\cdot13\cdot12}=3^{312}\)
QT
1
2 tháng 1 2021
Ta có: \(2^{-1}+\left(5^2\right)^3\cdot5^{-6}+32-2\cdot\left(-3\right)^2\cdot\dfrac{1}{9}\)
\(=\dfrac{1}{2}+5^6\cdot5^{-6}+32-2\cdot9\cdot\dfrac{1}{9}\)
\(=\dfrac{65}{2}-2+5^0\)
\(=\dfrac{61}{2}+1=\dfrac{63}{2}\)
14 tháng 10 2017
3.đặt biểu thức trên là A
ta có:
2A=2.(\(\dfrac{1}{3.5}\)+\(\dfrac{1}{5.7}\)+\(\dfrac{1}{7.9}\)+...+\(\dfrac{1}{2015.2017}\))
=>2A=\(\dfrac{2}{3.5}\)+\(\dfrac{2}{5.7}\)+\(\dfrac{2}{7.9}\)+....+\(\dfrac{2}{2015.2017}\)
=>2A=\(\dfrac{1}{3}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{9}\)+....\(\dfrac{1}{2015}\)-\(\dfrac{1}{2017}\)
=>2A=\(\dfrac{1}{3}\)-\(\dfrac{1}{2017}\)=\(\dfrac{2014}{6051}\)
=>A=\(\dfrac{2014}{6051}\):2=\(\dfrac{1007}{6051}\)
7 tháng 10 2017
\(\dfrac{10^2\cdot5^3}{8\cdot25^2}\)
\(=\dfrac{2^2\cdot5^2\cdot5^3}{2^3\cdot\left(5^2\right)^2}\)
\(=\dfrac{2^2\cdot5^5}{2^3\cdot5^4}\)
\(=\dfrac{5}{2}\)
D
1
6 tháng 12 2022
\(=\dfrac{5^3\left(2^3+2+1\right)}{55}-\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=5^2-\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=25-\dfrac{2}{3}\cdot\dfrac{6}{5}\)
=25-4/5
=24,2
21 tháng 12 2017
\(\dfrac{10^3+2.5^3+5^3}{55}=\dfrac{\left(2.5\right)^3+2.5^3+5^3}{55}=\dfrac{2.5^3+2.5^3+5^3}{55}=\dfrac{5^3\left(2+2+1\right)}{55}=\dfrac{5^2.5}{11}=\dfrac{5^3}{11}=\dfrac{125}{11}\)
21 tháng 12 2017
\(\dfrac{10^3+2.5^3+5^3}{55}=\dfrac{\left(2.5\right)^3+2.5^3+5^3}{55}\)
\(\Rightarrow\)\(\dfrac{5^3\left(2+2+2\right)}{55}\)=\(\dfrac{5^3}{11}\)=\(\dfrac{125}{11}\)
25
\(=\dfrac{1000+250+125}{55}=25\)