Question 337567
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{\frac{1}{n}} = \sqrt[n]{a}]


So we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt[6]{400}\ =\ 400^{\frac{1}{6}}]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(a^m\right)^n\ =\ a^{mn}]


So we can say


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 400^{\frac{1}{6}}\ =\ \left(400^^{\frac{1}{2}}\right)^{\frac{1}{3}}]


But square root 400 is 20, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(400^^{\frac{1}{2}}\right)^{\frac{1}{3}}\ =\ \left(20\right)^{\frac{1}{3}}]


Finally:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(20\right)^{\frac{1}{3}}\ =\ \sqrt[3]{20}]


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