(2x^3)(x^4)^2/8x^11

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will guide you through the simplification of the algebraic expression (2x^3)(x^4)^2 / 8x^11. We will break down the process step-by-step, making it easier to understand.

Understanding the Rules

Before we dive into the simplification, let's review some key rules of exponents:

• Product of powers: x^m * x^n = x^(m+n)
• Power of a power: (x^m)^n = x^(m*n)
• Division of powers: x^m / x^n = x^(m-n)

Step-by-Step Simplification

1. Simplify the power of a power: (x^4)^2 = x^(4*2) = x^8

2. Substitute the simplified expression: (2x^3)(x^8) / 8x^11

3. Apply the product of powers rule: 2x^(3+8) / 8x^11 = 2x^11 / 8x^11

4. Apply the division of powers rule: (2/8) * x^(11-11) = (1/4) * x^0

5. Remember x^0 = 1: (1/4) * 1 = 1/4

Final Result

Therefore, the simplified form of the expression (2x^3)(x^4)^2 / 8x^11 is 1/4.