GolfScript 3.673e+374\$ \approx 3.673 \times 10^{374} = 10 \uparrow\uparrow 2.70760 \$
'~'(.`*
I think the *
is allowed since it indicates string repetition, not multiplication.
Explanation: '~'(
will leave 126 (the ASCII value of "~") on the stack. Then copy the number, convert it to a string, and do string repetition 126 times. This gives 126126126126...
which is approximately 1.26 e+377
. The solution is 7 characters, so divide by 7^3
, for a score of approximately 3.673e+374