Question

find the value of a^-1 * a^2 * a^-3 *a^4 *.......(2004 terms)

Answer 1

=a^-1*a^2*a^-3*a^4...................(2004 terms)
=1/a*a^2*1/a^3*a^4...................(2004 terms)
={1/a*a^2}{1/a^3*a^4}........
{1/a^(2004-1)*a^2004}
={a}{a}............{1/a^2003*a^2004}
=a*a*a*a*..........................*a1002 times
=a^1002
These 'a' will be 1002 times.
Because all other 'a' will be getting cancel and for every one pair only one 'a' will be left.
Therefore no.of 'a' left is equals to 2004/2=1002
Hence value of given series is equals to a^1002