### Which is largest among 21/2, 31/3, 81/8 and 91/9.

31/3

Step by Step Explanation:
1. If we raise each of the given numbers 21/2, 31/3, 81/8 and 91/9 by same power, the largest number will still be found at the same position.
2. Let's raise each of the given numbers by a number which will make the powers of each number an integer. Such a number will be the LCM of 2, 3, 8, and 9 which is 72.
3. Raising each number by a power of 72, we get the following sequence of numbers:
272/2, 372/3, 872/8 and 972/9
236, 324, 89 and 98
236, 324, (23)9 and (32)8
236, 324,227 and 316
4. We can see that, 236 > 227 and 324 > 316
So, we only need to find the larger of 236 and 324,
Or the larger of (23)12 and (32)12,
Or the larger of 812 and 912.
5. Clearly 912 is larger. The number corresponding to 912 is 31/3. Thus 31/3 is the largest of all.