Whadayaknow, our shell of choice still has its limits:

# echo $((2**63-1))
9223372036854775807

# echo $((2**63))
-9223372036854775808

# file $SHELL
/bin/bash: ELF 64-bit LSB executable, x86-64, version 1 (SYSV) [...]

Zsh seems to have the same limit; ksh93 does:

ksh93$ echo $((2**1023))
8.98846567431157954e+307

ksh93$ echo $((2**1024))
inf

And csh seems to need some magic to do exponentiation at all.