Question
$$x^5 = 81$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^5 &= 81&& \text{move all terms to the left hand side } \\[1 em]x^5-81 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver