# 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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