(2x^5y)^3/36x^8y^6

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2x^5y)^3 / 36x^8y^6

This article will guide you through the process of simplifying the algebraic expression: (2x^5y)^3 / 36x^8y^6. We'll break down each step using the rules of exponents and algebraic manipulation.

Understanding the Problem

The expression involves exponents, parentheses, and division. To simplify it, we need to apply the following rules:

• Power of a Product: (ab)^n = a^n * b^n
• Power of a Power: (a^m)^n = a^(m*n)
• Division of Exponents: a^m / a^n = a^(m-n)

Step-by-Step Simplification

1. Simplify the numerator:

   • Apply the "Power of a Product" rule: (2x^5y)^3 = 2^3 * (x^5)^3 * y^3
   • Apply the "Power of a Power" rule: 2^3 * (x^5)^3 * y^3 = 8x^15y^3

2. Rewrite the expression: Now the expression is 8x^15y^3 / 36x^8y^6

3. Simplify the coefficients: 8 and 36 share a common factor of 4, so we can simplify: (8/4) / (36/4) = 2/9

4. Apply the division of exponents rule:

   • x^15 / x^8 = x^(15-8) = x^7
   • y^3 / y^6 = y^(3-6) = y^-3

5. Rewrite with positive exponents: Remember that y^-3 = 1/y^3

Final Simplified Expression

Combining all the simplified parts, the final simplified expression is: 2x^7 / 9y^3