2 min read Jun 17, 2024

Simplifying Expressions with Exponents

In mathematics, we often encounter expressions involving exponents. These expressions can be simplified using various rules of exponents. Let's consider the expression:


To simplify this expression, we'll use the following rules:

  • Power of a Product: (ab)^n = a^n * b^n
  • Power of a Power: (a^m)^n = a^(m*n)

Step 1: Apply the power of a product rule to each term.

This gives us: (x^3 * y^6)(x^6 * y^9)

Step 2: Apply the power of a power rule.

This simplifies to: x^(3+6) * y^(6+9)

Step 3: Combine the exponents.

This leads to the final simplified expression: x^9 * y^15

Therefore, the simplified form of (xy^2)^3(x^2y^3)^3 is x^9y^15.

Key Takeaways:

  • Understanding the rules of exponents is crucial for simplifying complex expressions.
  • By applying these rules step-by-step, we can systematically simplify expressions involving exponents.
  • The simplified form of the expression is a more concise representation of the original expression.