(5xy^3)^2(2x^5y^2)^3

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through the process of simplifying the expression (5xy^3)^2(2x^5y^2)^3. We'll use the rules of exponents to break down each step.

Understanding the Rules

Before we begin, let's review the key exponent rules we'll use:

• Product of Powers: (x^m)(x^n) = x^(m+n)
• Power of a Product: (xy)^n = x^n * y^n
• Power of a Power: (x^m)^n = x^(m*n)

Simplifying the Expression

1. Distribute the outer exponents:

   • (5xy^3)^2 = 5^2 * x^2 * (y^3)^2 = 25x^2y^6
   • (2x^5y^2)^3 = 2^3 * (x^5)^3 * (y^2)^3 = 8x^15y^6

2. Multiply the simplified terms:

   • (25x^2y^6)(8x^15y^6) = 25 * 8 * x^2 * x^15 * y^6 * y^6

3. Apply the Product of Powers Rule:

   • 200 * x^(2+15) * y^(6+6) = 200x^17y^12

Conclusion

Therefore, the simplified form of (5xy^3)^2(2x^5y^2)^3 is 200x^17y^12. Remember to apply the rules of exponents carefully, step by step, to reach the final answer.