To simplify ( \frac{5^2}{8^{5/8}} ) divided by ( 8^{2} ), first, rewrite it as ( \frac{5^2}{8^{5/8} \cdot 8^2} ). This can be simplified further since ( 8^2 = 8^{16/8} ), so we combine the exponents: ( 8^{5/8 + 16/8} = 8^{21/8} ). Thus, the expression simplifies to ( \frac{5^2}{8^{21/8}} ).
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