Think of it the other way!

Algebra Level 4

Consider the following system of linear equations:

{1+a+b+c+d+e=132+16a+8b+4c+2d+e=2243+81a+27b+9c+3d+e=31024+256a+64b+16c+4d+e=43125+625a+125b+25c+5d+e=5.\begin{cases} \begin{array}{rcrcrcrcrcrcrl} 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{array} \end{cases}

Evaluate

8bcd125ae. \left|\dfrac{8bcd}{125ae}\right|.

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