Answer:
25/81
Step-by-step explanation:
1000³ = (10³)³ = 10⁹ = 2⁹ × 5⁹
For a factor to be a perfect square, the exponents must be even. For example:
2⁰ × 5⁰, 2⁰ × 5², 2² × 5⁰, etc.
There are 5 even exponents between 0 and 9 for each 2 and 5. So the number of perfect square factors is 5×5 or 25.
The total number of factors is 9×9 or 81.
So the fraction of positive integer factors that are perfect squares is 25/81.
