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27 tháng 12 2019
\(\frac{10^3+2.5^3+5^3}{65}=\frac{10^3+5^3.\left(2+1\right)}{65}=\frac{10^3+5^3.3}{65}\)
= \(\frac{10^3+375}{65}=\frac{1375}{65}\)
DH
27 tháng 12 2019
\(\frac{10^3+2.5^3+5^3}{65}=\frac{1000+2.125+125}{65}=\frac{8.125+2.125+125.1}{65}=\frac{125\left(8+2+1\right)}{65}=\frac{125.11}{65}=\frac{1375}{65}=\frac{275}{13}\)
27 tháng 12 2019
\(\frac{10^3+2.5^3+5^3}{65}=\frac{1000+5^3.3}{65}=\frac{1000+375}{65}\)
= \(\frac{1375}{65}=\frac{275}{13}\)
27 tháng 12 2019
\(\frac{10^3+2.5^5+5^3}{65}\)
= \(\frac{\left(2.5\right)^3+2.5^5+5^3}{5.13}\)
= \(\frac{2^3.5^3+2.5^5+5^3}{5.13}\)
= \(\frac{5^3\left(2^3+2+1\right)}{5.13}\)
= \(\frac{5^2.11}{13}\)
= \(\frac{275}{13}\)
4 tháng 1 2022
\(\dfrac{45^{10}\cdot5^{20}}{75^{15}}=\dfrac{\left(3^2\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{3^{20}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{30}}=3^5=243\\ \dfrac{6^6+6^3+3^3+3^6}{-73}=\dfrac{46656+216+27+729}{-73}=-\dfrac{47628}{73}\\ \dfrac{27^7+3^{15}}{9^9-27}=\dfrac{\left(3^3\right)^7+3^{15}}{\left(3^2\right)^9-3^3}=\dfrac{3^{21}+3^{15}}{3^{18}-3^3}=\dfrac{3^{15}\left(3^6+1\right)}{3^3\left(3^{15}-1\right)}=\dfrac{3^5\cdot730}{3^{15}-1}\\ \dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}=1024\)
3 tháng 12 2018
\(A=\frac{7^{48}.5^{30}.2^8-5^{30}.7^{49}.2^{10}}{5^{29}.2^8.7^{48}}=\frac{7^{48}.5^{30}.2^8.\left(1-7.2^2\right)}{5^{29}.2^8.7^{48}}=5.\left(-27\right)=-135\)
Vậy \(A=-135\)
LM
0
DL
2
G
23 tháng 9 2020
\(A=\frac{6^{10}-3^9.2^8.5}{27^3.4^5+16^3.9^4}\)
\(=\frac{3^{10}.2^{10}-3^9.2^8.5}{\left(3^3\right)^3.\left(2^2\right)^5+\left(2^4\right)^3.\left(3^2\right)^4}\)
\(=\frac{3^{10}.2^{10}-3^9.2^8.5}{3^9.2^{10}+2^{12}.3^8}\)
\(=\frac{3^9.2^8.\left(3.2^2-1.1.5\right)}{3^8.2^{10}.\left(3.1+2^2\right)}\)
\(=\frac{3^9.2^8.7}{3^8.2^{10}.7}\)
\(=\frac{3}{2^2}=\frac{3}{4}\)
23 tháng 9 2020
Bài làm :
\(A=\frac{6^{10}-3^9.2^8.5}{27^3.4^5+16^3.9^4}\)
\(=\frac{\left(2.3\right)^{10}-3^9.2^8.5}{\left(3^3\right)^3.\left(2^2\right)^5+\left(2^4\right)^3.\left(3^2\right)^4}\)
\(=\frac{2^{10}.3^{10}-3^9.2^8.5}{3^9.2^{10}+2^{12}.3^8}\)
\(=\frac{2^8.3^9.\left(2^2.3-5\right)}{3^8.2^{10}.\left(3+2^2\right)}\)
\(=\frac{3.7}{2^2.7}\)
\(=\frac{3}{4}\)
Học tốt
19 tháng 7 2017
Ta có : \(\frac{1}{10.9}-\frac{1}{9.8}-.....-\frac{1}{2.1}\)
\(=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{9.8}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{8}-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\frac{8}{9}=\frac{-79}{90}\)
\(\frac{20^5.5^{10}}{100^5}=\frac{5^5.4^5.25^5}{100^5}=\frac{5^5.100^5}{100^5}=5^5=3125\)
\(\frac{20^5.5^{10}}{100^5}\)= \(\frac{5^5.4^5.5^5.5^5}{5^5.4^5.5^5}\)= \(5^5\)= \(3125\)