(18x^5yz)/(6xyz^4)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (18x^5yz) / (6xyz^4)

This article will guide you through the process of simplifying the algebraic expression (18x^5yz) / (6xyz^4).

Understanding the Basics

Before we start, let's review some key concepts:

• Variables: Letters representing unknown values (e.g., x, y, z).
• Coefficients: Numbers multiplying variables (e.g., 18, 6).
• Exponents: Numbers indicating how many times a base is multiplied by itself (e.g., x^5 means x multiplied by itself five times).

Simplifying the Expression

1. Divide the coefficients:

   • 18 divided by 6 equals 3.

2. Simplify the variables:

   • x: x^5 divided by x equals x^(5-1) = x^4.
   • y: y divided by y equals y^(1-1) = y^0 = 1. (Any number raised to the power of 0 equals 1).
   • z: z divided by z^4 equals z^(1-4) = z^(-3).

3. Combine the simplified terms:

   • The simplified expression becomes 3x^4 * 1 * z^(-3).

4. Express negative exponents in the denominator:

   • z^(-3) is equivalent to 1/z^3.

5. Final simplified expression:

   • The final simplified form of (18x^5yz) / (6xyz^4) is 3x^4 / z^3.

Key Points to Remember

• When dividing terms with the same base, subtract their exponents.
• Any number raised to the power of 0 equals 1.
• Negative exponents can be rewritten as their reciprocal with a positive exponent.

By following these steps, you can simplify complex algebraic expressions like (18x^5yz) / (6xyz^4) with ease.