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What fraction of the positive integer factors of 1000^3 are perfect squares? Express your answer as a common fraction.
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What fraction of the positive integer factors of 1000^3 are perfect squares? Express your answer as a common fraction.

User Deolinda
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1 Answer

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1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9

Perfect square factors have even exponents.

There are 5 even exponents between 0 and 9 for each 2 and 5.

Number of perfect square factors: 5x5 =25

Total number of factors: 9x9 =81

Fraction: 25/81

User Teflon
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