solve $a^{7} + \frac{1}{a^{9}} = ?$

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Solution

$a^{7} + \frac{1}{a^{9}} = \frac{a^{7 + 9} + 1}{a^{9}}$
$= \frac{a^{16} + 1}{a^{9}}$
$= \frac{1 + a^{16}}{a^{9}}$

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