Question 184117
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*[tex \LARGE \text{          }\math \frac{(a^{-2}b^3)^4 c^3}{b^{12}c^8}]


Strictly speaking you cannot 'solve' this expression.  You can, however, simplify it.


First, remove the parentheses by using:


*[tex \LARGE \text{          }\math (\alpha^n)^m = \alpha^{mn}]


So:


*[tex \LARGE \text{          }\math \frac{a^{-8}b^{12} c^3}{b^{12}c^8}]


Next, use:


*[tex \LARGE \text{          }\math \frac{\alpha^n}{\alpha^m} = \alpha^{n - m}]


and


*[tex \LARGE \text{          }\math \alpha^0 = 1]


So:


*[tex \LARGE \text{          }\math a^{-8}b^0 c^{-5}]


Lastly, use:


*[tex \LARGE \text{          }\math \alpha^{-n} = \frac{1}{\alpha^n}]


So:


*[tex \LARGE \text{          }\math \frac{1  }{a^8c^5}]



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