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NN
0
S
1
21 tháng 7 2016
\(\frac{35^{10}.5^{10}}{49^5.125}=\frac{5^{10}.7^{10}.5^{10}}{\left(7^2\right)^5.5^3}=\frac{5^{20}.7^{10}}{7^{10}.5^3}=\frac{5^{17}.1}{1.1}=5^{17}\)
12 tháng 9 2016
\(\frac{49^{24}.125^{10}.2^8-5^{30}.7^{49}.4^5}{5^{29}.16^2.7^{48}}\)
\(=\frac{\left(7^2\right)^{24}.\left(5^3\right)^{10}.2^8-5^{30}.7^{49}.\left(2^2\right)^5}{5^{29}.\left(2^4\right)^2.7^{48}}\)
\(=\frac{7^{48}.5^{30}.2^8-5^{30}.7^{49}.2^{10}}{5^{29}.2^8.7^{48}}\)
\(=\frac{7^{48}.5^{30}.2^8.\left(1-7.2^2\right)}{5^{29}.2^8.7^{48}}\)
\(=5.\left(1-7.4\right)\)
\(=5.\left(1-28\right)\)
\(=5.\left(-27\right)=-135\)
CM
1
I
21 tháng 9 2019
\(\frac{5^{32}.10^{43}}{16^{11}.125^{35}}=\frac{5^{32}.\left(2.5\right)^{43}}{2^4.\left(5^3\right)^{35}}=\frac{5^{32}.2^{43}.5^{43}}{2^4.5^{105}}=\frac{5^{32}.5^{43}.2^{39}.2^4}{2^4.5^{105}}=\frac{5^{75}.2^{39}}{5^{105}}=\frac{5^{75}.2^{39}}{5^{75}.5^{30}}=\frac{2^{39}}{5^{30}}\)
TG
3 tháng 8 2020
1) \(125^5:25^7\)
\(=\left(5^3\right)^5:\left(5^2\right)^7\)
\(=5^{15}:5^{14}\)
= 5
2) \(27^8:9^9\)
\(=\left(3^3\right)^8:\left(3^2\right)^9\)
\(=3^{24}:3^{18}\)
\(=3^6\)
3) \(36^5:6^8\)
\(=\left(6^2\right)^5:6^8\)
\(=6^{10}:6^8\)
\(=6^2\)
4) \(49^6:7^{10}\)
\(=\left(7^2\right)^6:7^{10}\)
\(=7^{12}:7^{10}=7^2\)
5) \(7^{20}:49^9\)
\(=7^{20}:\left(7^2\right)^9\)
\(=7^{20}:7^{18}=7^2\)
6) \(\frac{1}{2^{10}}:\frac{1}{8^3}\)
\(=\frac{1}{2^{10}}:\frac{1}{\left(2^3\right)^3}\)
\(=\frac{1}{2^{10}}:\frac{1}{2^9}=\frac{1}{2^{10}}.\frac{2^9}{1}=\frac{1}{2}\)
7) \(\left(-\frac{1}{2}\right)^{21}:\frac{1}{4^{10}}\)
\(=\frac{\left(-1\right)^{21}}{2^{21}}:\frac{1}{\left(2^2\right)^{10}}\)
\(=-\frac{1}{2^{21}}:\frac{1}{2^{20}}=-\frac{1}{2^{21}}.\frac{2^{20}}{1}\)
\(=-\frac{1}{2}\)
8) \(\frac{1}{16^5}:\left(-\frac{1}{2}\right)^{18}\)
\(=\frac{1}{\left(2^4\right)^5}:\frac{\left(-1\right)^{18}}{2^{18}}\)
\(=\frac{1}{2^{20}}:\frac{1}{2^{18}}\)
\(=\frac{1}{2^{20}}.\frac{2^{18}}{1}=\frac{1}{4}\)
9) \(\frac{1}{5^{30}}:\frac{1}{25^{14}}\)
\(=\frac{1}{5^{30}}:\frac{1}{\left(5^2\right)^{14}}\)
\(=\frac{1}{5^{30}}:\frac{1}{5^{28}}=\frac{1}{25}\)
3 tháng 2 2022
\(=\dfrac{7^{48}\cdot5^{30}\cdot2^8-5^{30}\cdot7^{49}\cdot2^{10}}{3^2\cdot2^2\cdot5^2\cdot7^{48}}\)
\(=\dfrac{7^{48}\cdot5^{30}\cdot2^8\left(1+7\cdot4\right)}{3^2\cdot2^2\cdot5^2\cdot7^{48}}=\dfrac{5^{28}\cdot2^6\cdot12}{3^2}=\dfrac{5^{28}\cdot2^8}{3}\)
\(35^{10}x5^{10}=\left(35x5\right)^{10}=175^{10}\)
\(49^5x125=7^3x5^3x7^7=35^3x7^7\)
\(\frac{35^{10}.5^{10}}{49^5.125}=\frac{5^{10}.7^{10}.5^{10}}{\left(7^2\right)^5.5^3}=\frac{5^{20}.7^{10}}{7^{10}.5^3}=5^{17}\)
chúc học tốt :)