Already we have learnt the concept of negative base and now let us proceed with the examples.

81/16
Here 81 can be written as 3 x 3 x 3 x 3 = 3^{4}
16 can be written as 2 x 2 x 2 x 2 = 2^{4}
we can write 81/16 as 3^{4}/2^{4}
3^{4}/2^{4} = (3)^{4}/(2)^{4} =(3/2)^{4}
Therefore we get result for 81/16 as (3/2)^{4}.

25/64
Now 25 can be written as 5 x 5,
64 can be written as 8 x 8.
We can write 25/64 as 52/82
25/64 = 5^{2}/8^{2} = (5/8)^{2}
Therefore we get the result for 25/64 as (5/8)^{2}.
Let us try to solve few more examples :

27/125

243/32
In the first example 27/125, here 27 = (3) x (3) x (3) = (3)^{3}
125 = 5 x 5 x 5 = (5)^{3}
27/125 = (3)^{3}/(5)^{3} = (3/5)^{3}.
Therefore we get the result for 27/125 as (3/5)^{3}.
Coming to second example 243/32, here 243 = (3) x (3) x (3) x (3) x (3) = (3)^{5}
32 = (2) x (2) x (2) x (2) x (2) = (2)^{5}
243/32 = (3)^{5}/(2)^{5} = (3/2)^{5}
Therefore we get the result for 243/32 as (3/2)^{5}.
In the above examples a^{m}/b^{m} = (a/b)^{m} property has used. 
The examples have been illustrated in the video below :