(3x^5)^2/27x^3

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (3x^5)^2 / 27x^3

This article will guide you through simplifying the algebraic expression (3x^5)^2 / 27x^3. We'll break down each step and explain the reasoning behind it.

Understanding the Rules of Exponents

Before we begin, let's refresh our understanding of exponent rules:

• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)
• Division of exponents with the same base: a^m / a^n = a^(m-n)

Step-by-Step Simplification

1. Simplify the numerator:

   • Apply the power of a product rule: (3x^5)^2 = 3^2 * (x^5)^2
   • Apply the power of a power rule: 3^2 * (x^5)^2 = 9x^(5*2) = 9x^10

2. Rewrite the expression:

   • The simplified expression now becomes: (9x^10) / 27x^3

3. Simplify the coefficients:

   • Divide both numerator and denominator by 9: (9x^10) / 27x^3 = (x^10) / 3x^3

4. Simplify the variables:

   • Apply the division of exponents rule: (x^10) / 3x^3 = (1/3) * x^(10-3) = (1/3) * x^7

The Final Answer

Therefore, the simplified form of the expression (3x^5)^2 / 27x^3 is (1/3)x^7 or x^7 / 3.