0.000006649= $a^{5}$
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MathBot Answer:
The solutions are given by the formula: \[a = \frac{\sqrt[5]{66490} \cos{\left(\frac{2 \pi k}{5} \right)}}{100} + \frac{\sqrt[5]{66490} \sin{\left(\frac{2 \pi k}{5} \right)}}{100} i\] where \(k\) is an integer in \(0 \le k < 5\).
There is \(1\) real solution.There are \(4\) solutions with nonzero imaginary part.
Real solutions: \[\begin{aligned}a &= \frac{\sqrt[5]{66490}}{100} \\&\approx 0.092161868\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}a &= \frac{\sqrt[5]{66490} \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{100} + \frac{\sqrt[5]{66490} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} \\&\approx 0.028479583 + 0.087651145 i\\a &= \frac{\sqrt[5]{66490} \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)}{100} + \frac{\sqrt[5]{66490} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100} \\&\approx -0.074560517 + 0.054171387 i\\a &= \frac{\sqrt[5]{66490} \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)}{100} - \frac{\sqrt[5]{66490} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{100} \\&\approx -0.074560517 -0.054171387 i\\a &= \frac{\sqrt[5]{66490} \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{100} - \frac{\sqrt[5]{66490} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{100} \\&\approx 0.028479583 -0.087651145 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).