Think of it the other way!

Algebra Level 4

Consider the following system of linear equations: \[\begin{cases} 1&+&a&+&b&+&c&+&d&+&e&=&1,\\ 32&+&16a&+&8b&+&4c&+&2d&+&e&=&2,\\ 243&+&81a&+&27b&+&9c&+&3d&+&e&=&3,\\ 1024&+&256a&+&64b&+&16c&+&4d&+&e&=&4,\\ 3125&+&625a&+&125b&+&25c&+&5d&+&e&=&5.\\ \end{cases}\]

Evaluate \[ \left|\dfrac{8bcd}{125ae}\right|.\]

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