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23^8*23^n=(23^5)^3. what is the answer

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23^8\cdot 23^n=(23^5)^3\implies \underset{same~base}{\stackrel{same~exponent}{23^(8+n)=23^((5)(3))}}\implies 8+n=(5)(3) \\\\\\ 8+n=15\implies n=7

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