The probability rolling nine fair dice and getting an even number on all nine dice

The probability is 1/512

This is my work
So you know a die has 3 odd and 3 even so to get a even it is 1/2 chance now you have 9 die so you have to multiply 1/2 by itself 9 times so it can be represented by 1/2^9 (1/2 to the power of 9), which 1*1=1 so just look at the 2. 2^9 is 2*2*2*2*2*2*2*2*2 which is 512. So 1/512 chance they are all even.