Exponential A.P

Number Theory Level 4

$\Huge {\color{#3D99F6}9}^{{\color{#20A900}8}^{{\color{#D61F06}7}^{{\color{#624F41}6}^{{\color{#302B94}5}^{{\color{magenta}4}^{{\color{grey}3}^{{\color{#BA33D6}2}^{\color{#E81990}1}}}}}}}}$

Find the last three digits of the number above.