Question 184370
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ 5^{2n} = (5^9)(5^{n+1})]


First use the rule:


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


To write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ 5^{2n} = 5^{9 + (n + 1)} = 5^{n + 10}]


Then use:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ a^m = a^n \ \ \Leftrightarrow\ \ m = n]


To write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ 2n = n + 10 \ \ \Rightarrow\ \ n = 10]


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