(-3a^3)^2(2ab)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (-3a^3)^2(2ab)^4

In mathematics, simplifying algebraic expressions involves using the rules of exponents and operations to reduce a complex expression to a more manageable form. Let's break down the simplification of the expression (-3a^3)^2(2ab)^4.

Understanding the Rules of Exponents

• Power of a product: (xy)^n = x^n * y^n
• Power of a power: (x^m)^n = x^(m*n)

Applying the Rules to Simplify

1. Distribute the exponents:

   • (-3a^3)^2 = (-3)^2 * (a^3)^2 = 9a^6
   • (2ab)^4 = 2^4 * a^4 * b^4 = 16a^4b^4

2. Multiply the simplified terms:

   • 9a^6 * 16a^4b^4 = 144a^(6+4)b^4 = 144a^10b^4

Final Simplified Expression

Therefore, the simplified form of (-3a^3)^2(2ab)^4 is 144a^10b^4.