(3xy^3)^2(xy)^6

Jasonbradley

2 min read

·

Jun 16, 2024

15

Share

Simplifying Expressions with Exponents: (3xy^3)^2(xy)^6

This article will guide you through simplifying the expression (3xy^3)^2(xy)^6. We'll break down the process step-by-step, using the rules of exponents.

Understanding the Rules of Exponents

To simplify this expression, we need to recall some key exponent rules:

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

Applying the Rules to Simplify

1. Simplify the first term: (3xy^3)^2

   Applying the power of a product rule: (3xy^3)^2 = 3^2 * x^2 * (y^3)^2

   Then, applying the power of a power rule: 3^2 * x^2 * (y^3)^2 = 9x^2y^6

2. Simplify the second term: (xy)^6

   Using the power of a product rule: (xy)^6 = x^6 * y^6

3. Multiply the simplified terms together:

   9x^2y^6 * x^6y^6

4. Combine like terms:

   9x^(2+6) * y^(6+6) = 9x^8y^12

Conclusion

Therefore, the simplified form of (3xy^3)^2(xy)^6 is 9x^8y^12. By carefully applying the rules of exponents, we were able to break down the expression and arrive at a concise solution.