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a) \(T=\frac{9^{14}\times25^6\times8^7}{18^{12}\times625^3\times24^3}\)
\(=\frac{\left(3^2\right)^{14}\times25^6\times\left(2^3\right)^7}{\left(2\times3^2\right)^{12}\times\left(25^2\right)^3\times\left(3\times2^3\right)^3}\)
\(=\frac{3^{28}\times25^6\times2^{21}}{2^{12}\times3^{24}\times25^6\times3^3\times2^9}\)
\(=\frac{3^{28}\times25^6\times2^{21}}{\left(2^{12}\times2^9\right)\times\left(3^{24}\times3^3\right)\times25^6}\)
\(=\frac{3^{28}\times25^6\times2^{21}}{2^{21}\times3^{27}\times25^6}=3\)
b) \(A=\frac{5\times4^{15}\times9^9-4\times3^{20}\times8^9}{5\times2^9\times6^{19}-7\times2^{29}\times27^6}\)
\(=\frac{5\times\left(2^2\right)^{15}\times\left(3^2\right)^9-2^2\times3^{20}\times\left(2^3\right)^9}{5\times2^9\times\left(2\times3\right)^{19}-7\times2^{29}\times\left(3^3\right)^6}\)
\(=\frac{5\times2^{30}\times3^{18}-2^2\times3^{20}\times2^{27}}{5\times2^9\times2^{19}\times3^{19}-7\times2^{29}\times3^{18}}\)
\(=\frac{5\times2^{30}\times3^{18}-2^{29}\times3^{20}}{5\times2^{28}\times3^{19}-7\times2^{29}\times3^{18}}\)
\(=\frac{2^{29}\times3^{18}\times\left(5\times2-3^2\right)}{2^{28}\times3^{18}\times\left(5\times3-7\times2\right)}\)
\(=\frac{2\times\left(10-9\right)}{15-14}=\frac{2\times1}{1}=2\)
1)
a) \(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{24}.5^{12}.3^3.2^9}=\frac{3}{5^2}=\frac{3}{25}\)
Bài 2:
\(\frac{abab}{cdcd}=\frac{ab.101}{cd.101}=\frac{ab}{cd};\frac{ababab}{cdcdcd}=\frac{ab.10101}{cd.10101}=\frac{ab}{cd}\)
Vậy \(\frac{ab}{cd}=\frac{abab}{cdcd}=\frac{ababab}{cdcdcd}\)
\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)
\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{2^{12}.\left(3^2\right)^{12}.\left(5^4\right)^3.3^3.\left(2^3\right)^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}\)
\(=\frac{3}{5^2}\)
\(=\frac{3}{25}\)
TL:
\(\frac{4.5+4.11}{4.3-8.7}=\frac{20+44}{12-56}=\frac{64}{-44}=-\frac{16}{1}=-16\)
\(\frac{4^6.3^4.9^5}{6^{12}.15}=\frac{2^{12}.3^{14}}{2^{12}.3^{13.5}}=\frac{3}{5}\)
Học tốt
\(H=\frac{4116-14}{10290-35}=\frac{14.294-14}{35.294-35}=\frac{14.\left(294-1\right)}{35.\left(294-1\right)}=\frac{14.293}{35.293}=\frac{2}{5}\)
\(K=\frac{29.101-101}{2.19.101+4.101}=\frac{101.\left(29-1\right)}{101.\left(38+4\right)}=\frac{28}{42}=\frac{2}{3}\)
\(I=\frac{1313-1717}{303}=\frac{13.101-17.101}{3.101}=\frac{101.\left(13-17\right)}{3.101}=\frac{-4}{3}\)
\(M=\frac{12-24.3}{1-35}=\frac{12-12.2.3}{-34}=\frac{12.\left(1-6\right)}{-34}=\frac{-60}{-34}=\frac{30}{17}\)
\(H\)\(=\) \(\frac{4116-14}{10290-35}\)
\(=\) \(\frac{4102}{10255}\)
\(=\) \(\frac{4102:2051}{10255:2051}\)
\(=\) \(\frac{2}{5}\)
\(K=\frac{2929-101}{2.1919+404}\)
\(=\) \(\frac{2828}{4242}\)
\(=\) \(\frac{2828:1414}{4242:1414}\)
\(=\) \(\frac{2}{3}\)
\(M=\frac{12-24.3}{1-35}\)
\(=\) \(\frac{-60}{-34}\)
\(=\) \(\frac{60}{34}\)
\(=\) \(\frac{30}{17}\)
:D
a) \(\frac{9}{33-3}=\frac{1}{3}\)
b) \(\frac{7}{100+6\times100}=\frac{1}{100}\)
c) \(\frac{11\times22+33\times36+55\times60}{22\times24+66\times72+110\times120}=\frac{1}{4}\)
d) \(\frac{9^4\times27^5\times3^6\times4^4}{3^8\times81^4\times243\times8^2}=4\)
e) \(\frac{199919991999}{200020002000}=\frac{1999}{2000}\)
A = \(\frac{9^{14}\times25^5\times8^7}{18^{12}\times625^2\times24^3}\)
A = \(\frac{\left(3^2\right)^{14}\times\left(5^2\right)^5\times\left(2^3\right)7}{\left(2.3^2\right)^{12}\times\left(5^4\right)^3\times\left(2^3.3\right)^3}\)
A = \(\frac{3^{28}\times5^{10}\times2^{21}}{2^{12}\times3^{24}\times5^{12}\times2^9\times3^3}\)
A = \(\frac{3^{28}\times5^{10}\times2^{21}}{\left(3^{24}.3^3\right)\times5^{12}\times\left(2^{12}\times2^9\right)}\)
A = \(\frac{3^{28}\times5^{10}\times2^{21}}{3^{27}\times5^{12}\times2^{21}}\)
A = \(\frac{3}{5^2}\)
A = \(\frac{3}{25}\)
\(\dfrac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}\)
\(=\dfrac{3^{28}\cdot5^{10}\cdot2^{21}}{\left(2\cdot3^2\right)^{12}\cdot\left(5^4\right)^3\cdot\left(2^3\cdot3\right)^3}\)
\(=\dfrac{2^{21}\cdot3^{28}\cdot5^{10}}{2^{12}\cdot3^{24}\cdot5^{12}\cdot2^9\cdot3^3}\)
\(=\dfrac{2^{21}}{2^{21}}\cdot\dfrac{3^{28}}{3^{27}}\cdot\dfrac{5^{10}}{5^{12}}=\dfrac{3}{5^2}=\dfrac{3}{25}\)