The space shuttle can travel about 8*10 to the power of 5 centimeters per second. Is it more appropriate to report this rate as 8*10 to the power of 5 centimeters per second or 8 kilometers per second?

According to the National Institute of Science and Technology, the MKS (meter Kilogram Second) sytem of units is preferred over the CGS (centimeter gram Second) system. Kilometer is NOT in either system but I'd choose kilometer. And so it would be 8 x 10^5 km/sec.

Still, if you want to adhere to the International System of Units, then you would say 8 x 10^8 meters per second.