\(\frac{\left(\frac{2}{3}\right)^3.\left(-\frac{3}{4}\right)^2.\left(-1\right)^{2003}}{\left(\frac{2}{5}\right)^2.\left(-\frac{5}{12}\right)^3}\)
\(=\frac{\left(\frac{2}{3}\right)^3.\left(\frac{3}{4}\right)^2.\left(-1\right)}{\left(\frac{2}{5}\right)^2.\left(-\frac{5}{12}\right)^3}\)
\(=\frac{\left(\frac{2}{3}\right)^3.\left(\frac{3}{4}\right)^2}{\left(\frac{2}{5}\right)^2.\left(\frac{5}{12}\right)^3}\)
\(=\frac{\frac{2^3}{3^3}.\frac{3^2}{4^2}}{\frac{2^2}{5^2}.\frac{5^3}{12^3}}\)
\(=\frac{\frac{2^3.3^2}{3^3.4^2}}{\frac{2^2.5^3}{5^2.12^3}}\)
\(=\frac{2^3.3^2.5^2.12^3}{3^3.4^2.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.\left(4.3\right)^3}{3^3.\left(2^2\right)^2.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.4^3.3^3}{3^3.2^4.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.\left(2^2\right)^3.3^3}{3^3.2^4.2^2.5^3}\)
\(=\frac{2^3.3^2.5^2.2^6.3^3}{3^3.2^4.2^2.5^3}\)
\(=\frac{2^9.3^5.5^2}{3^3.2^6.5^3}\)
\(=\frac{2^3.3^2}{5}\)
\(=\frac{8.9}{5}\)
\(=\frac{72}{5}.\)
Chúc bạn học tốt!
