(5²)–⁸ ——— 5–¹⁵

To simplify the expression \((5^2)^{-8} \div 5^{-15}\), we can follow the rules of exponents.

1. Simplify the numerator: \[ (5^2)^{-8} = 5^{2 \cdot -8} = 5^{-16} \]

2. Now, rewrite the expression: \[ \frac{5^{-16}}{5^{-15}} \]

3. When dividing two expressions with the same base, we subtract the exponents: \[ 5^{-16 - (-15)} = 5^{-16 + 15} = 5^{-1} \]

4. Finally, we can simplify \(5^{-1}\) to: \[ \frac{1}{5} \]

Thus, the final result is: \[ \frac{1}{5} \]