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\(\left(\dfrac{2}{3}\right)^3.\left(\dfrac{-3}{4}\right)^2.\left(-1\right)^{2013}=\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)=-\dfrac{1}{6}\)
\(\left(\dfrac{1}{5}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}=\dfrac{1}{5^{12}}.\dfrac{1}{4^{20}}=5^{-12}.4^{-20}=125^{-4}.1024^{-4}=\left(125.1024\right)^{-4}=128000^{-4}\)
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.2^{10}.5}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3+1\right)}=\dfrac{2.6}{3.7}=\dfrac{4}{7}\)
a) \(\frac{7.12^3+2.12^3}{4^6.3^{11}}=\frac{12^3.\left(7+2\right)}{\left(2^2\right)^6.3^{11}}=\frac{\left(2^2.3\right)^3.3^2}{2^{12}.3^{11}}=\frac{2^6.3^5}{2^{12}.3^{11}}=\frac{1}{2^6.3^6}=\frac{1}{6^6}\)
\(\frac{-17.10+17.6}{18.11+18.6}=\frac{17.\left(-10+6\right)}{18.\left(11+6\right)}=\frac{17.\left(-4\right)}{18.17}=\frac{-2}{9}\)
\(\frac{6.7.8.10}{9.12.14.15}=\frac{2.3.7.2^3.2.5}{3^2.3.2^2.2.7.3.5}=\frac{2^5.3.5.7}{2^3.3^4.5.7}=\frac{2^2}{3^3}=\frac{4}{27}\)
phần b viết khó hiểu, phải viết phân số như a đàng hoàng
Phân tích ra : VD : 415=(22)15=22.15=230
Nếu làm thế này thì sẽ dể hơn vì sẽ có nhiều lũy thừa giống nhau và dễ chiệt tiêu hơn nhé bạn >
Bạn đăng lên H.vn thử xem . Trên đấy có nhiều người trả lời giúp hơn đấy mà còn nhanh hơn nữa.
\(a,\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right).\)
\(=\left(\dfrac{21}{60}+\dfrac{44}{60}-\dfrac{75}{60}\right):\left(\dfrac{99}{180}-\dfrac{104}{180}\right).\)
\(=\left(\dfrac{65}{60}-\dfrac{75}{60}\right):\left(-\dfrac{5}{180}\right).\)
\(=-\dfrac{10}{60}:\left(-\dfrac{5}{180}\right).\)
\(=-\dfrac{1}{6}:\left(-\dfrac{1}{36}\right).\)
\(=-\dfrac{1}{6}.\left(-36\right).\)
\(=\dfrac{-1.\left(-36\right)}{6}=\dfrac{36}{6}=6.\)
Vậy......
\(b,\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}.\)
\(=\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}.\)
\(=\dfrac{5}{8}:\dfrac{15}{16}.\)
\(=\dfrac{5}{8}.\dfrac{16}{15}=\dfrac{5.16}{8.15}=\dfrac{1.2}{1.3}=\dfrac{2}{3}.\)
Vậy......
c, (làm tương tự câu b).
~ Học tốt!!! ~
1) \(\frac{3^{10}+6^2}{5\cdot3^8+20}=\frac{3^{10}+3^2\cdot2^2}{5\cdot3^8+5\cdot2^2}=\frac{3^2\left(3^8+2^2\right)}{5\left(3^8+2^2\right)}=\frac{9}{5}\)
2) \(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{28^{15}\cdot3^{17}}{28^{16}\cdot3^{16}}=\frac{3}{28}\)
1. \(\dfrac{9.5^{20}.27^9-3.9^{15}:25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\dfrac{3^2.5^{20}.3^{27}-3.3^{30}.5^{18}}{7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}}\)
\(=\dfrac{3^{29}.5^{20}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}\)
\(=\dfrac{3^{28}.5^{18}.\left(5^2-3^2\right)}{3^{29}.5^{18}.\left(7-5\right)}\)
\(=\dfrac{5^2-3^2}{7-5}=\dfrac{16}{2}=8\)
2.\(\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{-4}\right)^{20}=\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}\)
\(=\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{2}^2\right)^{20}=\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{2}\right)^{40}\)
\(=\left(\dfrac{1}{2}\right)^{55}\)
3.\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)
\(=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)
\(=\dfrac{1-3}{1+5}=\dfrac{-2}{6}=\dfrac{-1}{3}\)
Chúc học tốt!!
\(A=\dfrac{2.3.\left(2^3\right)^6.3^{20}-2^2.5.3^{20}.\left(2^2\right)^8}{7.2^2.2^{16}.\left(3^2\right)^{10}-2.3^2.2^{18}.\left(3^3\right)^6}\)
\(=\dfrac{2.3.2^{18}.3^{20}-5.2^2.3^{20}.2^{16}}{7.2^2.2^{16}.3^{20}-2.3^2.2^{18}.3^{18}}=\dfrac{2^{19}.3^{21}-5.2^{18}.3^{20}}{7.2^{18}.3^{20}-2^{20}.3^{20}}\)
\(=\dfrac{2^{18}.3^{20}\left(2.3-5\right)}{2^{18}.3^{20}.\left(7-2^2\right)}=\dfrac{2.3-5}{7-4}=\dfrac{1}{3}\)