(9x^5y^6)(4xy)/6x^2y^4

Jasonbradley

3 min read

·

Jun 16, 2024

22

Share

Simplifying Algebraic Expressions: (9x^5y^6)(4xy)/6x^2y^4

This article will guide you through simplifying the algebraic expression (9x^5y^6)(4xy)/6x^2y^4. We'll break down the process step by step to help you understand the concepts involved.

Understanding the Basics

Before we delve into the simplification, let's review a few key rules of exponents:

• Multiplication of exponents with the same base: When multiplying exponents with the same base, add the powers. For example: x^m * x^n = x^(m+n)
• Division of exponents with the same base: When dividing exponents with the same base, subtract the powers. For example: x^m / x^n = x^(m-n)

Simplifying the Expression

1. Multiply the coefficients: Start by multiplying the coefficients in the numerator: (9 * 4) = 36.

2. Combine the x terms: Apply the rule for multiplying exponents with the same base: x^5 * x * x = x^(5+1+1) = x^7.

3. Combine the y terms: Similarly, apply the rule for multiplying exponents with the same base: y^6 * y * y = y^(6+1+1) = y^8.

4. Simplify the denominator: Apply the rule for dividing exponents with the same base: x^7 / x^2 = x^(7-2) = x^5.

   • Similarly, y^8 / y^4 = y^(8-4) = y^4.

5. Combine the simplified terms: Now we have: (36x^7y^8) / (6x^2y^4)

6. Final simplification: Divide the coefficient in the numerator by the coefficient in the denominator: 36/6 = 6.

   • This gives us: 6x^5y^4

The Simplified Expression

Therefore, the simplified form of (9x^5y^6)(4xy)/6x^2y^4 is 6x^5y^4.