(2x^3)(8x^5)/4x^6

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (2x^3)(8x^5)/4x^6

This article will guide you through simplifying the algebraic expression (2x^3)(8x^5)/4x^6.

Understanding the Basics

Before we start simplifying, let's recap some fundamental rules of algebra:

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

Simplifying the Expression

1. Multiply the terms in the numerator: (2x^3)(8x^5) = 16x^(3+5) = 16x^8

2. Rewrite the expression: The expression now becomes 16x^8 / 4x^6.

3. Divide the coefficients and the variables:

   • 16 / 4 = 4
   • x^8 / x^6 = x^(8-6) = x^2

4. Combine the results: The simplified expression is 4x^2.

Conclusion

By applying basic rules of exponents and simplifying step by step, we have successfully reduced the complex expression (2x^3)(8x^5)/4x^6 to 4x^2.