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KL
1
VM
17 tháng 2 2020
\(\frac{\left(\frac{2}{3}\right)^3.\left(-\frac{3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\frac{2}{5}\right)^2.\left(-\frac{5}{12}\right)^3}\)
\(=\frac{\left(\frac{2}{3}\right)^3.\left(\frac{3}{4}\right)^2.\left(-1\right)}{\left(\frac{2}{5}\right)^2.\left(-\frac{5}{12}\right)^3}\)
\(=\frac{\left(\frac{2}{3}\right)^3.\left(\frac{3}{4}\right)^2}{\left(\frac{2}{5}\right)^2.\left(\frac{5}{12}\right)^3}\)
\(=\frac{\frac{2^3}{3^3}.\frac{3^2}{4^2}}{\frac{2^2}{5^2}.\frac{5^3}{12^3}}\)
\(=\frac{\frac{2^3.3^2}{3^3.4^2}}{\frac{2^2.5^3}{5^2.12^3}}\)
\(=\frac{2^3.3^2.5^2.12^3}{3^3.4^2.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.\left(4.3\right)^3}{3^3.\left(2^2\right)^2.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.4^3.3^3}{3^3.2^4.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.\left(2^2\right)^3.3^3}{3^3.2^4.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.2^6.3^3}{3^3.2^4.2^2.5^3}\)
\(=\frac{2^9.3^5.5^2}{3^3.2^6.5^3}\)
\(=\frac{2^3.3^2}{5}\)
\(=\frac{8.9}{5}\)
\(=\frac{72}{5}.\)
Chúc bạn học tốt!
27 tháng 7 2017
\(\frac{\left(\frac{2}{3}\right)^3.\left(\frac{-3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\frac{2}{5}\right)^2.\left(\frac{-5}{12}\right)^3}\)=\(\frac{\frac{8}{27}.\frac{9}{16}.-1}{\frac{4}{25}.\frac{-125}{1728}}\)=\(\frac{\frac{-1}{6}}{-\frac{5}{432}}\)=\(\frac{-1}{6}:\frac{-5}{432}=\frac{-1}{6}.-\frac{432}{5}=\frac{72}{5}\)
Bài này dễ mà bn
HH
26 tháng 6 2018
Giải:
\(B=\dfrac{\left(\dfrac{2}{3}\right)^3.\left(-\dfrac{3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\dfrac{2}{5}\right)^2.\left(-\dfrac{5}{12}\right)^3}\)
\(\Leftrightarrow B=\dfrac{\left(\dfrac{2}{3}\right)^3.\left(\dfrac{3}{4}\right)^2.\left(-1\right)}{\left(\dfrac{2}{5}\right)^2.\left(-\dfrac{5}{12}\right)^3}\)
\(\Leftrightarrow B=\dfrac{\left(\dfrac{2}{3}\right)^3.\left(\dfrac{3}{4}\right)^2}{\left(\dfrac{2}{5}\right)^2.\left(\dfrac{5}{12}\right)^3}\)
\(\Leftrightarrow B=\dfrac{\dfrac{2^3.3^2}{3^3.4^2}}{\dfrac{2^2.5^3}{5^2.12^3}}\)
\(\Leftrightarrow B=\dfrac{2^3.3^2.5^2.12^3}{3^3.4^2.2^2.5^3}\)
\(\Leftrightarrow B=\dfrac{2^3.3^2.5^2.2^6.3^3}{3^3.2^4.2^2.5^3}\)
\(\Leftrightarrow B=\dfrac{2^9.3^5.5^2}{3^3.2^6.5^3}\)
\(\Leftrightarrow B=\dfrac{2^3.3^2}{5}\)
\(\Leftrightarrow B=\dfrac{72}{5}\)
Vậy ...
DT
26 tháng 6 2018
\(B=\dfrac{\left(\dfrac{2}{3}\right)^3.\left(-\dfrac{3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\dfrac{2}{5}\right)^2.\left(-\dfrac{5}{12}\right)^3}=\dfrac{\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)}{\dfrac{4}{25}.\left(-\dfrac{125}{1728}\right)}=\dfrac{\dfrac{-1}{6}}{\dfrac{-5}{432}}=\dfrac{72}{5}\)
\(\frac{\frac{2^3}{3^3}.\frac{\left(-3\right)^2}{4^2}.\left(-1\right)}{\frac{2^2}{5^2}.\frac{\left(-5\right)^3}{12^3}}=\frac{\frac{8}{27}.\frac{9}{16}.\left(-1\right)}{\frac{4}{25}.\frac{-125}{1728}}=\frac{\frac{-72}{432}}{\frac{-500}{43200}}=\frac{\frac{-1}{6}}{\frac{-5}{432}}=\frac{-1}{6}.\frac{432}{-5}=14,4\)
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