Exponential A.P

Number Theory Level 4

\[\Huge {\color{blue}9}^{{\color{green}8}^{{\color{red}7}^{{\color{brown}6}^{{\color{indigo}5}^{{\color {magenta}4}^{{\color{grey}3}^{{\color{violet}2}^{\color{pink}1}}}}}}}}\]

Find the last three digits of the number above.