Calculate the value of the expression: (5^(-2))^(-8) / 5^(-15)

Okay, let's calculate the value of the expression step by step. First, let's simplify the numerator. We have $$(5^{-2})^{-8}$$. When raising a power to a power, we multiply the exponents: $$(5^{-2})^{-8} = 5^{(-2) \times (-8)} = 5^{16}$$ Now we have the expression: $$\frac{5^{16}}{5^{-15}}$$ When dividing exponential expressions with the same base, we subtract the exponents: $$\frac{5^{16}}{5^{-15}} = 5^{16 - (-15)} = 5^{16 + 15} = 5^{31}$$ So the final answer is $$5^{31}$$. Answer: $$5^{31}$$