(2a^3b^4c^3)^2 X (4a^2bc^3)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (2a^3b^4c^3)^2 x (4a^2bc^3)

This article will guide you through simplifying the algebraic expression (2a^3b^4c^3)^2 x (4a^2bc^3). We will break down the process step by step, explaining the rules and properties involved.

Understanding the Properties

Before we begin, let's refresh our memory on a couple of key properties:

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

Simplifying the Expression

1. Simplify the first term:

   • Apply the power of a product property to (2a^3b^4c^3)^2:
     • (2a^3b^4c^3)^2 = 2^2 * (a^3)^2 * (b^4)^2 * (c^3)^2 = 4a^6b^8c^6

2. Multiply the simplified terms:

   • Now we have: 4a^6b^8c^6 * 4a^2bc^3
   • Combine the coefficients: 4 * 4 = 16
   • Apply the product of powers property for each variable:
     • a^6 * a^2 = a^(6+2) = a^8
     • b^8 * b = b^(8+1) = b^9
     • c^6 * c^3 = c^(6+3) = c^9

3. Final Result:

   • Combining all the terms, the simplified expression is: 16a^8b^9c^9

Summary

By applying the power of a product and product of powers properties, we simplified the expression (2a^3b^4c^3)^2 x (4a^2bc^3) to 16a^8b^9c^9. This process demonstrates the importance of understanding and utilizing algebraic properties for efficient simplification.