(a^3b)^4(ab^6)^2

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (a^3b)^4(ab^6)^2.

Understanding the Rules of Exponents

Before we begin simplifying, let's refresh our memory on the key rules of exponents:

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

Step-by-Step Simplification

1. Apply the power of a power rule:

   • (a^3b)^4 = a^(34) * b^(14) = a^12 * b^4
   • (ab^6)^2 = a^(12) * b^(62) = a^2 * b^12

2. Substitute the simplified terms back into the original expression:

   • (a^12 * b^4) * (a^2 * b^12)

3. Apply the product of powers rule:

   • a^(12+2) * b^(4+12) = a^14 * b^16

Final Result

Therefore, the simplified form of (a^3b)^4(ab^6)^2 is a^14 * b^16.