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How many positive perfect cube factors does \(3^55^{10}\) have?

So what I'm doing right now is checking with a calculator whether a divisor is a perfect cube...Is there a faster way to do this? (btw, I know it is a repost but the answer for that question was incorrect.)

Guest Oct 31, 2018

#1**+1 **

You calculate perfect cubes as follows:

Take the exponent / 3 (use integer part only) + 1 = 5/3 + 1 =2, and 10/3 + 1 = 4. Then multiply them together:

So, 2 x 4 = 8 perfect Cubes in 3^5 x 5^10 as follows: (1^3, 3^3, 5^3, 15^3, 25^3, 75^3, 125^3, 375^3) =8

P.S. These Perfect Cubes are divisors(factors) of 3^5 * 5^10.

Guest Oct 31, 2018

edited by
Guest
Oct 31, 2018