Question

Which is larger 9^9/10^9 or 9^10/10^10?

(Answer without the calculating it)

Answer 1

Assuming [9^9/10^9] is greater than [9^10/10^10]
Now if [9^9/10^9]/[9^10/10^10] is greater than 1 than the assumption is true
=[9^9/10^9]/[9^10/10^10]
=(9^9/10^9)*(10^10/9^10)
=(1/1)*(10/9)
=10/9 is greater than 1 hence 9^9/10^9 > 9^10/10^10

OR

9^9/10^9 - 9^10/10^10
= (10*9^9 - 9^10)/10^10
= 9^9*(10 - 9)/10^10
= 9^9*(1)/10^10
= 9^9*/10^10 is positive which means our initial assumption was right ie, 9^9/10^9 > 9^10/10^10