(5a^2b^3c^4)^4(6a^3b^4c^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (5a^2b^3c^4)^4(6a^3b^4c^2)

This article will guide you through the process of simplifying the algebraic expression (5a^2b^3c^4)^4(6a^3b^4c^2). We'll break down the steps involved to make it easier to understand.

Understanding the Properties of Exponents

Before we begin, let's recall some essential properties of exponents:

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

Simplifying the Expression

1. Simplify the first term:

   • (5a^2b^3c^4)^4 = 5^4 * (a^2)^4 * (b^3)^4 * (c^4)^4
   • Applying the power of a power rule: 5^4 * a^8 * b^12 * c^16

2. Simplify the second term:

   • 6a^3b^4c^2 remains as it is.

3. Multiply the simplified terms together:

   • 5^4 * a^8 * b^12 * c^16 * 6a^3b^4c^2

4. Combine like terms:

   • (5^4 * 6) * (a^8 * a^3) * (b^12 * b^4) * (c^16 * c^2)

5. Apply the product of powers rule:

   • 3750 * a^11 * b^16 * c^18

Final Result

Therefore, the simplified form of the expression (5a^2b^3c^4)^4(6a^3b^4c^2) is 3750a^11b^16c^18.