Simplifying (8a^5)^2
In mathematics, simplifying expressions is a crucial skill. One common type of expression involves exponents. Let's take a look at how to simplify (8a^5)^2.
Understanding the Rules
To simplify this expression, we need to understand the following rules:
 Power of a product rule: (ab)^n = a^n * b^n
 Power of a power rule: (a^m)^n = a^(m*n)
Applying the Rules

Apply the power of a product rule: (8a^5)^2 = 8^2 * (a^5)^2

Apply the power of a power rule: 8^2 * (a^5)^2 = 64 * a^(5*2)

Simplify: 64 * a^(5*2) = 64a^10
Conclusion
Therefore, the simplified form of (8a^5)^2 is 64a^10. Remember to follow the order of operations and apply the appropriate exponent rules when simplifying expressions.