Question 339871
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{\frac{m}{n}} = \sqrt[n]{a^m}\ =\ \left(\sqrt[n]{a}\right)^m]


Take the cube root of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^{\frac{1}{4}}\ =\ -2]


Raise both sides to the fourth power:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 16]


Or, if you happen to be a arithmetic masochist,


Raise both sides to the fourth power:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^3\ =\ 4096]


Take the cube root of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 16]


Bear in mind if you try to work this backwards from the solution to get the original problem, you are going to end up with an either/or situation because:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 16^{\frac{3}{4}}\ =\ \pm8]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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