To simplify the expression $(2^5)^2$, use the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

$(2^5)^2 = 2^{5 \cdot 2} = 2^{10}$

Next, calculate $2^{10}$:

$2^{10} = 1024$

So, the simplified expression is:

$1024$

Would you like more details, or do you have any questions?

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Here are 5 related questions:

1. How would you simplify $(3^4)^3$?
2. What is the result of $(5^2)^4$?
3. Can you simplify $(7^3)^2$?
4. How do you evaluate $(2^8)^1$?
5. What is the simplified form of $(10^3)^2$?

Tip: When simplifying expressions involving exponents, use the power of a power rule to combine exponents efficiently before performing calculations.