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

Jasonbradley

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Jun 16, 2024

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

This article will guide you through simplifying the algebraic expression (3b^-2)^2(a^2b^4)^3. We will utilize the rules of exponents to break down the expression step by step.

Understanding the Rules of Exponents

Before we begin, let's review some key rules of exponents:

• Product of powers: x^m * x^n = x^(m+n)
• Power of a power: (x^m)^n = x^(m*n)
• Power of a product: (x*y)^n = x^n * y^n
• Negative exponent: x^-n = 1/x^n

Simplifying the Expression

1. Apply the power of a power rule:

   • (3b^-2)^2 = 3^2 * (b^-2)^2 = 9b^-4
   • (a^2b^4)^3 = (a^2)^3 * (b^4)^3 = a^6 * b^12

2. Combine the results from step 1:

   • 9b^-4 * a^6 * b^12

3. Apply the product of powers rule:

   • 9 * a^6 * b^(-4+12)

4. Simplify the exponents:

   • 9a^6b^8

Final Result

The simplified form of the expression (3b^-2)^2(a^2b^4)^3 is 9a^6b^8.