All your base (and unbase) are belong to us

base.pl

use v6;

sub base(@rad, @a) { [+] ([\*] 1, @rad.reverse) Z* @a.reverse };

sub unbase(@rad, $val is copy) {
    reverse gather {
        for @rad.reverse {
            take $val % $_;
            last unless ($val /= $_).=Int;
        }
        take $val if $val;
    }
}

use Test;

is base([10, 10, 10, 10], <4 1 2 3>), 4123;
is base([0, 3, 12], <3 0 1>), 109;
is base([1736, 3, 12], <3 0 1>), 109;

is unbase(<10 10 10 10>, 1234), <1 2 3 4>;
is unbase(<24 60 60>, 12345), <3 25 45>;
is unbase(<24 60 60>, 123456), <1 10 17 36>;
is unbase(<24 60 60>, 3), 3;