Constant Product?

If the number of ordered quintuplets \((x_1,x_2,x_3,x_4,x_5)\) such that \[\displaystyle\prod_{i=1}^{5} x_i=1458000\] is of the form \(2^a \times 3^b \times 5^c \times 7^d\), then find \(a+b+c+d\).

Details and Assumptions:

  • \(x_1,x_2,x_3,x_4,x_5 \in \mathbb{N}\)
  • \(a,b,c,d \in \mathbb{N}\)
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