(xy^2)^3(x^2y^3)^3

Jasonbradley

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Jun 17, 2024

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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:

(xy^2)^3(x^2y^3)^3

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.