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**