Question 279573
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What equation?  I see a rational expression,  but I don't see an equals sign anywhere.  Not having an equals sign, you can't "solve" anything.  The best I can do is help you simplify the expression.


Remember


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{-n}\ =\ \frac{1}{a^n}], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(2s^{-1}t^3\right)^{-3}}{\left(6s^2t^{-4}\right)^{-3}}\ =\ \frac{\left(6s^2t^{-4}\right)^{3}}{\left(2s^{-1}t^3\right)^{3}}]


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



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(6s^2t^{-4}\right)^{3}}{\left(2s^{-1}t^3\right)^{3}} =\ \frac{216s^6t^{-12}}{8s^{-3}t^9} ]


Again, apply


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{-n}\ =\ \frac{1}{a^n}], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{216s^6t^{-12}}{8s^{-3}t^9}\ =\ \frac{216s^6s^3}{8t^9t^{12}}]


Now apply:


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{216s^6s^3}{8t^9t^{12}}\ =\ \frac{216s^9}{8t^{21}}]


Finally divide 8 into 216:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{216s^9}{8t^{21}}\ =\ \frac{27s^9}{t^{21}}]


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