The culture contains 2*10^8 bacteria before it was exposed to ionizing radiation which kills 99.99% of the bacteria. The number of bacteria left after the radiation would be:
final number= initial number * (100%- radiation kill rate)
final number= 2*10^8 *(100%-99.99%)
final number= 2*10^8 *(0.01%)
final number= 2*10^8 * 10^-6
final number= 2*10^(8-6)
final number= 2*10^2