Note that exa now officially means 10^18 even in the context of
data processing. The prefixes
kilo,
mega,
giga,
tera,
peta, exa,
zetta,
yotta always refer to powers of 10.
To refer to powers of 2^10 (powers of 1024), use the new binary prefixes kibi, mebi, gibi, tebi, pebi, and exbi. So
1 exabyte = 1 EB = 10^18 bytes
1 exbibyte = 1 EiB = (1024)^6 bytes
These new prefixes were created in December 1998 by the International Electrotechnical Commission: see the node prefixes for binary multiples for fuller explanation.
It is permissible to use "exabyte" to mean exbibyte on a temporary basis until industry standards have shifted to the new terms.