Question 219489
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3^9\cdot\left(x^2y\right)^{-2}}{3^3\cdot x^{-4}y}]


Start with *[tex \Large \left(a^m\right)^n = a^{mn}] and *[tex \Large a = a^1], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3^9\cdot x^{\left(2\cdot -2\right)}y^{\left(1\cdot -2\right)}}{3^3\cdot x^{-4}y}\ =\ \frac{3^9\cdot x^{-4}y^{-2}}{3^3\cdot x^{-4}y}]


Next use *[tex \Large \frac{a}{a} = 1], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3^9\cdot y^{-2}}{3^3\cdot y}]


Next use *[tex \Large a^{-n} = \frac{1}{a^n}] and *[tex \Large a^m\cdot a^n = a^{m+n}], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3^9}{3^3\cdot y^2\cdot y}\ =\ \frac{3^9}{3^3\cdot y^{2+1}}\ =\ \frac{3^9}{3^3\cdot y^3}]


Finally, use *[tex \Large \frac{a^m}{a^n}\ =\ a^{m-n}], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3^{9-3}}{y^3}\ =\ \frac{3^{6}}{y^3}\ =\ \frac{729}{y^3}]



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