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![](https://rs.olm.vn/images/avt/0.png?1311)
#)Giải :
a)\(2009^{\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-15^3\right)}=2009^{\left(1000-1^3\right)...\left(1000-10^3\right)...\left(1000-15^3\right)}=2009^0=1\)
b)\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...0...\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(-2\right)\left(-1\frac{1}{2}\right)\left(-1\frac{1}{3}\right)....\left(-1\frac{1}{2010}\right)=-2.\frac{-3}{2}.\frac{-4}{3}...\frac{-2011}{2010}=2.\frac{3}{2}.\frac{4}{3}...\frac{2011}{2010}\)
=2011
\(=\frac{\left(-2\right)\left(-3\right)...\left(-2010\right)\left(-2011\right)}{\left(-2\right)\left(-3\right)...\left(-2010\right)}=-2011\)