%5E3-simplified.jpeg "(a^2)^3 Simplified")
Simplifying (a^2)^3
In mathematics, simplifying expressions often involves applying the rules of exponents. One common scenario is simplifying expressions like (a^2)^3. Let's break down how to do this:
Understanding the Rules of Exponents
The key rule to remember here is the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents.
Mathematically: (a^m)^n = a^(m*n)
Applying the Rule
In our example, we have (a^2)^3. Applying the power of a power rule:
- (a^2)^3 = a^(2*3)
- (a^2)^3 = a^6
Therefore, the simplified form of (a^2)^3 is a^6.
Example:
Let's say a = 2. We can verify our simplification by plugging in the value:
- (a^2)^3 = (2^2)^3 = 4^3 = 64
- a^6 = 2^6 = 64
As we can see, both expressions result in the same answer, confirming our simplification.
Key Takeaways:
- Power of a power rule: (a^m)^n = a^(m*n)
- Remember to multiply the exponents when simplifying expressions with nested powers.
- You can verify your simplification by plugging in a value for the variable.