%5E3.jpeg "(ab^2)^3")
Understanding (ab^2)^3
In mathematics, simplifying expressions like (ab^2)^3 involves applying the rules of exponents. Here's a breakdown of how to approach this:
The Power of a Product Rule
The power of a product rule states that when raising a product to a power, we raise each factor to that power:
(ab)^n = a^n * b^n
Applying the Rule
Let's apply this rule to our expression (ab^2)^3:
- Identify the factors: In this case, we have two factors: 'a' and 'b^2'.
- Raise each factor to the power of 3:
- a^3
- (b^2)^3
- Simplify the second factor: We apply the power of a power rule which states (x^m)^n = x^(m*n)
- (b^2)^3 = b^(2*3) = b^6
The Final Result
Therefore, the simplified expression for (ab^2)^3 is:
a^3 * b^6
This process illustrates how understanding the rules of exponents allows us to simplify complex expressions and manipulate them efficiently.