To solve the expression $(2^5)^2$, follow these steps:

1. First, calculate $2^5$: $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$

2. Now, square the result: $(32)^2 = 32 \times 32 = 1024$

So, $(2^5)^2 = 1024$.

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. What is the value of $(3^4)^3$?
2. How do you simplify $(a^3)^2$ for any positive integer $a$?
3. Calculate $2^{10}$ and explain how it relates to the original problem.
4. What is $(2^5)^3$?
5. How do you simplify expressions of the form $(x^m)^n$?

Tip: When dealing with exponents, remember that $(a^m)^n = a^{m \times n}$.