The expression you need to simplify is $(5^8)^2$.

To simplify this using the "power of a power" rule in exponents, which states:

$(a^m)^n = a^{m \cdot n}$

In your case:

$(5^8)^2 = 5^{8 \cdot 2} = 5^{16}$

So, the simplified expression is $5^{16}$.

Would you like more details or have any questions about this?

Here are five related questions to expand on this topic:

1. What is the general rule for multiplying exponents with the same base?
2. How do you simplify expressions with exponents when dividing?
3. What happens when you raise a number to the power of zero?
4. How do you simplify an expression like $(a^m \cdot b^n)^p$?
5. What is the difference between powers of a power and powers of a product?

Tip: When raising a power to another power, multiply the exponents to simplify the expression.