Final answer:
To count how many integers from 1 to 1000 are not perfect squares, perfect cubes, or perfect fifth powers, you can use a for loop and check each number using mathematical functions.
Step-by-step explanation:
To determine the count of integers between 1 and 1000 that are neither perfect squares, perfect cubes, nor perfect fifth powers, we can employ a for loop to iterate through the numbers in that range. Within the loop, we can use the Math.sqrt() function to check if a number is a perfect square, the Math.cbrt() function to check if a number is a perfect cube, and the Math.pow() function to check if a number is a perfect fifth power.
We can create variables to keep track of the count of non-perfect squares, non-perfect cubes, and non-perfect fifth powers. For each number, if it is not a perfect square, not a perfect cube, and not a perfect fifth power, we can increment the respective count variable.
After iterating through all the numbers, we can display the count of non-perfect squares, non-perfect cubes, and non-perfect fifth powers.