(10xy^5z^3)(3x^4y^6z^3)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (10xy^5z^3)(3x^4y^6z^3)

This article explores the process of simplifying the given expression: (10xy^5z^3)(3x^4y^6z^3).

Understanding the Basics

The expression involves multiplying monomials. Monomials are algebraic expressions with only one term, consisting of a coefficient and variables raised to non-negative exponents.

Key Principles:

• Coefficient Multiplication: Multiply the coefficients together.
• Variable Multiplication: Multiply variables with the same base by adding their exponents.

Step-by-Step Simplification

1. Multiply the coefficients: 10 * 3 = 30

2. Multiply the x terms: x^1 * x^4 = x^(1+4) = x^5

3. Multiply the y terms: y^5 * y^6 = y^(5+6) = y^11

4. Multiply the z terms: z^3 * z^3 = z^(3+3) = z^6

Final Result

Combining the results from each step, we get the simplified expression:

30x^5y^11z^6