Question 229035
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(-27x^9\right)^{\frac{1}{3}}]


First recognize that *[tex \Large -27\ =\ (-3)^3]
(*[tex \Large -3\ \times\ -3\ \times\ -3\ =\ 9\ \times\ -3\ =\ -27])


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left((-3)^3x^9\right)^{\frac{1}{3}}]


Then use:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (a^m)^n\ =\ a^{m\cdot n}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (-3)^{3\cdot\frac{1}{3}}x^{9\cdot\frac{1}{3}}]


Now use


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^1 = a]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -3x^3]




John
*[tex \LARGE e^{i\pi} + 1 = 0]
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