$3$ , $4$ tower

Number Theory Level 2

$\huge \color{#3D99F6}{3}^{\color{#20A900}{4}^{\color{#D61F06}{5}^{\color{#69047E}{6}^{\color{#624F41}{7}^{\color{#E81990}{8}}}}}}$

What's the last digit of the number above?

333, 444 tower