Question 391134
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*[tex \LARGE w^5] is incorrect.


Think of it this way.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w^2\ =\ w\,\cdot\,w]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^3\ =\ x\,\cdot\,x\,\cdot\,x]


So let *[tex \Large x\ =\ w^2] and substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (w^2)^3\ =\ (w^2)(w^2)(w^2)\ = (w\,\cdot\,w)(w\,\cdot\,w)(w\,\cdot\,w)\ =\ w\,\cdot\,w\,\cdot\,w\,\cdot\,w\,\cdot\,w\,\cdot\,w\ =\ w^6]


Capisce?


In general,


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


whereas


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^n\,\cdot\,a^m\ =\ a^{n+m}]


One more thing:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(w^2\right)^3]


is NOT an equation.  It is necessary (but not always sufficient) for a thing to contain an equals sign (=) in order for the thing to be an equation.


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