(a^3b^2)^3

2 min read Jun 16, 2024
(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

  1. Identify the factors: In our expression, the factors are a^3 and b^2.
  2. Apply the rule: Using the power of a product rule, we get: (a^3b^2)^3 = (a^3)^3 * (b^2)^3
  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.

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