How many different rational numbers between 1/1000 and 1000 can be written either as a power of 2 or as a power of 3, where the exponent is a (possibly negative) integer?
+118608 Why don't you just count them?
2^10=1024 that is too big so 1/2^10 is too little
2^9 = 512 that is the biggest power of 2 and 2^-9 is the smallest So that is 9+9+1=19
(9 negative, nine positive the one extra one is 2^0=3^0=1)
Now do the same for powers of 3
and find the total :)
If you want more help then ask. But show me what you have tried. :)
+118608 I got 32. Does that seem right?
It is nice to hear from you 
Lets see.
I already got 19 for the twos
32-19=13
Mmm that does not look good. It should be an even number.
maybe you counted 1 twice?
Lets see.
3^6 = 729 the next one will be bigger than 1000.
So I think the answer is 19+12= 31
You counted 1 twice 
