%5E3.jpeg "(a^3b^2)^3")
Simplifying (a^3b^2)^3
In mathematics, simplifying expressions often involves using the rules of exponents. One such expression is (a^3b^2)^3. Let's break down how to simplify this expression.
Understanding the Rules of Exponents
The key rule we'll use is the power of a product rule:
(xy)^n = x^n * y^n
This rule states that when you raise a product to a power, you raise each factor in the product to that power.
Applying the Rule to (a^3b^2)^3
- Identify the factors: In our expression, the factors are a^3 and b^2.
- Apply the rule: Using the power of a product rule, we get: (a^3b^2)^3 = (a^3)^3 * (b^2)^3
- Simplify: To further simplify, we use the power of a power rule: (x^m)^n = x^(m*n) Applying this rule, we get: (a^3)^3 * (b^2)^3 = a^(33) * b^(23) = a^9 * b^6
Final Result
Therefore, the simplified form of (a^3b^2)^3 is a^9b^6.