The number of ducks in a pond is equal to the square root of the number of fish, and the number of turtles is equal to the cube root of the number of fish. The number of fish in the pond is more than 1 but less than 100. There are no fractional or negative numbers of ducks, fish, or turtles.

There are 64 fish, 8 ducks and 4 turtles.

Explanation:

From the question, there can be from 2 to 99 fish in the pond. However, there cannot be fractions in the number of fish, ducks or turtles. Hence, the number of fish must have both of a perfect square and perfect cube. The perfect squares from 2 to 99 are 4, 9, 16, 25, 36, 49, 64 and 81. The perfect cubes from 2 to 99 are 8, 27 and 64. Since only 64 fits both criteria, the number of fish is 64. The number of ducks is the square root of number of fish, which is the square root of 64. The square root of 64 can be either positive 8 or negative 8. However, there cannot be negative numbers, so there are 8 ducks in total. The number of turtles is the cube root of the number of fish, which is the cube root of 64 and it is 4.