Find the last two digits of $9^{8^7}$. (by convention, exponent towers are evaluated from the top down, so $9^{8^7} = 9^{(8^7)}$.)

The answer 
by convention, exponent towers are evaluated from the top down, so $9^{8^7} = 9^{(8^7)}$
{(8^7) =  2097152, 9^{(8^7)}$ = infinity, but we know that 
a^x = exp(lna^x)=exp x(lna)
(8^7) = exp 7 (ln8), and ln8=2.07, (8^7) = exp (7*2.07)=  2099059.61496
finally 9^{(8^7)} = 9^(2099059.61496) = exp(2099059.61496 ln9)