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\(a,\) \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+\left(2.3\right)^9.2^3.3.5}{2^{12}.3^{12}-\left(2.3\right)^{11}}\)
\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{\left(2^{12}.3^{10}\right)\left(1+5\right)}{\left(2^{11}.3^{11}\right)\left(2.3-1\right)}\)
\(=\frac{\left(2^{12}.3^{10}\right).6}{\left(2^{11}.3^{11}\right).5}\)
\(=\frac{2.6}{3.5}\)
\(=\frac{2.2}{5}\)
\(=\frac{4}{5}\)
\(b,\) \(\frac{2^{15}.9^4}{6^3.8^3}\)
\(=\frac{2^{15}.3^8}{2^3.3^3.2^9}\)
\(=\frac{2^{15}.3^8}{2^{12}.3^3}\)
\(=2^3.3^5\)
\(=8.243\)
\(=1944\)
Chúc bạn học tốt ^^
a) \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+6^9.120}{\left(2^3\right)^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+6^9.120}{2^{12}.3^{12}-6^{11}}=\frac{6^{10}.4+6^{10}.20}{6^{12}-6^{11}}=\frac{6^{10}.\left(4+20\right)}{6^{11}.\left(6-1\right)}=\frac{6^{11}.4}{6^{11}.5}=\frac{4}{5}\)
b) \(\frac{2^{15}.9^4}{6^3.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^3.3^3.2^9}=\frac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5=1944\)
c) \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(4.2\right)^{10}+4^{10}}{\left(2^3\right)^4+4^6.4^5}=\frac{4^{10}.2^{10}+4^{10}}{2^{12}+4^6.4^5}=\frac{4^{10}.\left(2^{10}+1\right)}{4^6+4^6.2^{10}}=\frac{4^{10}.\left(2^{10}+1\right)}{4^6.\left(1+2^{10}\right)}=\frac{4^{10}}{4^6}=4^4=256\)
a, Ta có: \(\frac{0,8^5}{0,4^6}=\frac{\left(0,4.2\right)^5}{0,4^6}=\frac{0,4^5.2^5}{0,4^6}\) \(=\frac{2^5}{0,4}=80\)
b, Ta có: \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\) \(=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{12}\left(2^{18}+2^8\right)}{2^{12}\left(1+2^{10}\right)}\)
\(=\frac{2^{18}+2^8}{1+2^{10}}=\frac{2^8\left(2^{10}+1\right)}{2^{10}+1}=2^8\)
c, Ta có: \(\frac{2^{15}.9^4}{6^3.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^3.3^3.2^9}\) \(=\frac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5=1944\)
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)=\(\frac{\left(2.4\right)^{10}+4^{10}}{\left(2.4\right)^{10}+4^{11}}\)=\(\frac{2^{10}.4^{10}+4^{10}.1}{2^{10}.4^{10}+4^{10}.4}\)=\(\frac{4^{10}\left(2^{10}+1\right)}{4^{10}\left(2^{10}+4\right)}\)=\(\frac{4^{10}.1025}{4^{10}.1028}\)=\(\frac{1025}{1028}\)
Bạn Hương có 27 viên bi, bạn Hiền có số bi bằng 1/3 số bi của bạn Hương. Trung bình cộng số bi của hai bạn là bao nhiêu?
10 điểm
36 viên
15 viên
30 viên
18 viên
Bài 1:
a) Ta có: \(\frac{3}{8}+\frac{-5}{6}\)
\(=\frac{3}{8}-\frac{5}{6}\)
\(=\frac{9}{24}-\frac{20}{24}\)
\(=-\frac{11}{24}\)
b) Ta có: \(\frac{15}{12}-\frac{-1}{4}\)
\(=\frac{15}{12}+\frac{1}{4}\)
\(=\frac{15}{12}+\frac{3}{12}\)
\(=\frac{18}{12}=\frac{3}{2}\)
Bài 2:
a) Ta có: \(-\frac{1}{12}-\left(2\frac{5}{8}-\frac{1}{3}\right)\)
\(=-\frac{1}{12}-\frac{21}{8}+\frac{1}{3}\)
\(=\frac{-2}{24}-\frac{63}{24}+\frac{8}{24}\)
\(=\frac{-57}{24}\)
\(=-\frac{19}{8}\)
b) Ta có: \(\frac{-5}{6}-\left(\frac{-3}{8}+\frac{1}{10}\right)\)
\(=\frac{-5}{6}+\frac{3}{8}-\frac{1}{10}\)
\(=\frac{-100}{120}+\frac{45}{120}-\frac{12}{120}\)
\(=\frac{-67}{120}\)
c) Ta có: \(-1.75-\left(\frac{-1}{9}-2\frac{1}{18}\right)\)
\(=-\frac{7}{4}+\frac{1}{9}+\frac{37}{18}\)
\(=\frac{-63}{36}+\frac{4}{36}+\frac{74}{36}\)
\(=\frac{15}{36}=\frac{5}{12}\)
b) \(\frac{2^9.4^{10}}{8^8}=\frac{2^9.\left(2^2\right)^{10}}{\left(2^3\right)^8}=\frac{2^9.2^{20}}{2^{24}}=\frac{2^{29}}{2^{24}}=2^5=32.\)
Chúc bạn học tốt!