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^(mn)
Simplifying the Expression

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

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

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.

Simplify the denominator: Apply the rule for dividing exponents with the same base: x^7 / x^2 = x^(72) = x^5.
 Similarly, y^8 / y^4 = y^(84) = y^4.

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

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.