\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{-\left(2.5\right)^5}{3^5}.\frac{\left(3.2\right)^4}{5^4}=\frac{-2^5.5^5.3^4.2^4}{3^5.5^4}=\frac{-2^9.5}{3}\)

Ta có: \(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{\left(-10\right)^5}{3^5}.\frac{\left(-6\right)^4}{5^4}=\frac{\left(-2.5\right)^5}{3^5}.\frac{\left(-2.3\right)^4}{5^4}=\frac{\left(-2\right)^5.5^5}{3^5}.\frac{\left(-2\right)^5.3^4}{5^4}=\frac{\left(-2\right)^5.5^5.\left(-2\right)^4.3^4}{3^5.5^4}\)\(=\frac{\left[\left(-2\right)^5.\left(-2\right)^4\right].5^5.3^4}{3^5.5^4}=\frac{\left(-2\right)^9.5}{3}=\frac{-512.5}{3}=-\frac{2560}{3}\)

Chuk bn hk tốt! 

a,A=0-2+4-6+...+2010-2012

A=-2+-2+...+-2+-2 (503 cặp)

A=-2.503

A=-1006

có kết quả r mà

Số số hạng là (2012-4):4+1=503(số)

=>\(A=503\cdot\dfrac{\left(2012+4\right)}{2}\cdot\dfrac{1}{1000}\cdot\dfrac{6+9+10}{12}\)

\(=503\cdot1008\cdot\dfrac{1}{1000}\cdot\dfrac{25}{12}=\dfrac{21}{10}\cdot503=\dfrac{10563}{10}\)