Solution:
First, let’s prime factorize 6,480:
6,480 = 81 x 80 = 3^4 x 2^4 x 5
Recall that, in order for a number to be a perfect cube, all exponents of the prime factors must be positive multiples of 3. We see that √n must be (at least) 3^2 x 2^2 x 5^2 so that 6,480√n is (at least) 3^6 x 2^6 x 5^3, a perfect cube. Therefore, we have
√n = 3^2 x 2^2 x 5^2
n = 3^4 x 2^4 x 5^4 = (3 x 2 x 5)^4 = 30^4
Answer: E
