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HN
1
15 tháng 8 2016
Rút gọn:
\(A=5^0+5^1+5^2+...+5^{99}+5^{50}\)
\(5A=5^1+5^2+5^3+...+5^{51}\)
\(5A-A=\left(5^1+5^2+5^3+...+5^{51}\right)-\left(5^0+5^1+5^2+...+5^{50}\right)\)
\(4A=5^{51}-5^0\)
\(=>A=\left(5^{51}-5^0\right):4\)
Vậy : \(A=\left(5^{51}-5^0\right):4\)
LQ
1
3 tháng 2 2022
\(=\dfrac{-5^7\cdot2^5\cdot2^3\cdot5^3}{-5^{16}\cdot2^8\cdot2^9}=\dfrac{5^7\cdot2^{11}}{5^{16}\cdot2^{19}}=\dfrac{1}{5^9\cdot2^8}\)
BD
2
BB
7 tháng 2 2020
-5B=(-5)1+(-5)2+(-5)3+...+(-5)2018
-5B-B=[(-5)1+(-5)2+...+(-5)2018] - [(-5)0+(-5)1+...+(-5)2017]
-6B=(-5)2018-(-5)0 = (-5)2018-1
B= [(-5)2018-1]:-6
Anh học tốt nha ( em mới lớp 6)
NH
0
PA
5 tháng 7 2016
a.
\(\frac{2^7\times9^3}{6^5\times8^2}=\frac{2^7\times\left(3^2\right)^3}{\left(2\times3\right)^5\times\left(2^3\right)^2}=\frac{2^7\times3^6}{2^5\times3^5\times2^6}=\frac{3}{2^4}=\frac{3}{16}\)
b.
\(\frac{6^3+3\times6^2+3^3}{-13}=\frac{\left(2\times3\right)^3+3\times\left(3\times2\right)^2+3^3}{-13}=\frac{2^3\times3^3+3\times3^2\times2^2+3^3}{-13}=\frac{8\times3^3+3^3\times4+3^3}{-13}\)\(=\frac{3^3\times\left(8+4+1\right)}{-13}=\frac{27\times13}{-13}=-27\)
c.
\(\frac{5^4\times20^4}{25^5\times4^5}=\frac{\left(5\times20\right)^4}{\left(25\times4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
d.
\(\left(\frac{5^4-5^3}{125^4}\right)=\frac{5^3\times\left(5-1\right)}{\left(5^3\right)^4}=\frac{5^3\times4}{5^{12}}=\frac{4}{5^9}\)
NN
5 tháng 7 2016
a)\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}\)
b)\(\frac{6^3+3.6^2+3^3}{-13}=\frac{6.6^2+3.6^2+3^3}{-13}=\frac{6^2.\left(6+3\right)+3^3}{-13}=\frac{6^2.9+3^3}{-13}=\frac{6^2.3^2+3.3^2}{-13}=\frac{3^2.\left(6^2+3\right)}{-13}=\frac{3^2.39}{-13}=3^2.\left(-3\right)=-27\)
c)\(\frac{5^4.20^4}{25^5.4^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
17 tháng 10 2018
C = \(\frac{2}{3}\sqrt{144}-\left(-\frac{3}{4}\right)\div\sqrt{\frac{225}{144}}\)
C = \(\frac{2}{3}.12+\frac{3}{4}\div\frac{5}{4}\)
C = \(8+\frac{3}{5}\)
C = \(8\frac{3}{5}\)
D = \(\frac{4^6.25^5-2^{12}.25^4}{2^{12}.5^8-10^8.64}\)
D = \(\frac{\left(2^2\right)^6.\left(5^2\right)^5-2^{12}.\left(5^2\right)^4}{2^{12}.5^8-\left(2.5\right)^8.2^6}\)
D = \(\frac{2^{12}.5^{10}-2^{12}.5^8}{2^{12}.5^8-2^8.5^8.2^6}\)
D = \(\frac{2^{12}.5^8.\left(25-1\right)}{2^{12}.5^8.\left(1-2^2\right)}\)
D = \(\frac{24}{-3}\)
D = \(-8\)
T
18 tháng 10 2018
\(C=\frac{2}{3}\sqrt{144}-\left(\frac{-3}{4}\right):\sqrt{\frac{225}{144}}\)
\(=\frac{2}{3}\cdot12+\frac{3}{4}:\frac{5}{4}\)
\(=8+\frac{3}{4}\cdot\frac{4}{5}\)
\(=8+\frac{3}{5}\)
\(=\frac{40}{5}+\frac{3}{4}=\frac{43}{5}\)
\(D=\frac{4^6\cdot25^5-2^{12}\cdot25^4}{2^{12}\cdot5^8-10^8\cdot64}=\frac{\left(2^2\right)^6\cdot\left(5^2\right)^5-2^{12}\cdot\left(5^2\right)^4}{2^{12}\cdot5^8-\left(2\cdot5\right)^8\cdot2^6}\)
\(=\frac{2^{12}\cdot5^{10}-2^{12}\cdot5^8}{2^{12}\cdot5^8-2^{14}\cdot5^8}=\frac{5^8\left(2^{12}\cdot5^2-2^{12}\right)}{5^8\left(2^{12}-2^{14}\right)}\)
\(=\frac{2^{12}\cdot5^2-2^{12}}{2^{12}-2^{14}}=\frac{2^{12}\left(5^2-1\right)}{2^{12}\left(1-2^2\right)}=\frac{24}{-3}=-8\)
4 tháng 8 2019
\(M=\frac{-2x}{3}+3x\left(\frac{x}{6}-\frac{-2}{9}-\frac{7}{5}\right)-\frac{5x}{2}\left(\frac{x}{5}-\frac{4}{5}\right)\)
\(M=\frac{-2x}{3}+3x\left[\frac{x}{6}-\left(-\frac{2}{9}\right)-\frac{7}{5}\right]-\frac{5x}{4}\left(\frac{x}{5}-\frac{4}{5}\right)\)
\(M=\frac{-2x}{3}+3x\left(\frac{x}{6}+\frac{2}{9}-\frac{7}{5}\right)-\frac{5x}{2}\left(\frac{x}{5}-\frac{4}{5}\right)\)
\(M=-\frac{2x}{3}+3x\left(\frac{x}{6}-\frac{53}{45}\right)-\frac{5x}{2}.\frac{x-4}{5}\)
\(M=-\frac{2x}{3}+3x\left(\frac{x}{6}-\frac{53}{45}\right)-\frac{5x\left(x-4\right)}{10}\)
\(M=-\frac{2x}{3}+3x\left(\frac{x}{6}-\frac{53}{45}\right)-\frac{x\left(x-4\right)}{2}\)
\(M=-\frac{2x}{3}+\frac{x^2}{2}-\frac{53x}{15}-\frac{x\left(x-4\right)}{2}\)
\(M=\left(-\frac{2x}{3}-\frac{53x}{15}\right)+\frac{x^2}{2}-\frac{x\left(x-4\right)}{2}\)
\(M=-\frac{21x}{5}+\frac{x^2}{2}-\frac{x\left(x-4\right)}{2}\)
\(M=\frac{-2.21x+5x^2-5x\left(x-4\right)}{10}\)
\(M=\frac{-42x+5x^2-5x\left(x-4\right)}{10}\)
\(M=\frac{-x\left[42-5x+5\left(x-4\right)\right]}{10}\)
\(M=\frac{-x\left(42-5x+5x-20\right)}{10}\)
\(M=\frac{-x\left(42-20\right)}{10}\)
\(M=\frac{-x.22}{10}\)
\(M=-\frac{22x}{10}\)
\(M=-\frac{11x}{5}\)