Simplifying (a^5)^2
In mathematics, simplifying expressions is a crucial skill. This involves using the rules of exponents to express the expression in its simplest form. Today, we'll tackle the simplification of (a^5)^2.
Understanding the Rules
Before we dive into the simplification, let's review the essential rules of exponents we'll use:
 Product of Powers: a^m * a^n = a^(m+n)
 Power of a Power: (a^m)^n = a^(m*n)
 Negative Exponent: a^n = 1/a^n
Simplifying (a^5)^2
Now, let's apply these rules to our expression:

Apply the Power of a Power rule: (a^5)^2 = a^(5*2)

Simplify the exponent: a^(5*2) = a^10

Apply the Negative Exponent rule: a^10 = 1/a^10
Therefore, the simplified form of (a^5)^2 is 1/a^10.
Conclusion
Simplifying expressions like (a^5)^2 involves understanding and applying the fundamental rules of exponents. By systematically applying these rules, we can arrive at a concise and easytounderstand expression.