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(2x^5y^3)(3x^3y)

2 min read Jun 16, 2024
(2x^5y^3)(3x^3y)

Simplifying Expressions: (2x^5y^3)(3x^3y)

This article explores the simplification of the expression (2x^5y^3)(3x^3y) using the rules of exponents.

Understanding the Rules of Exponents

Before diving into the simplification, let's review the key rules of exponents:

  • Product of powers: When multiplying powers with the same base, add the exponents. For example, x^m * x^n = x^(m+n).
  • Power of a product: When raising a product to a power, distribute the exponent to each factor. For example, (xy)^n = x^n * y^n.

Simplifying the Expression

  1. Rearrange the terms: We can rearrange the terms in the expression to group similar variables: (2x^5y^3)(3x^3y) = (2 * 3) (x^5 * x^3)(y^3 * y)

  2. Apply the product of powers rule:

    • For the x terms: x^5 * x^3 = x^(5+3) = x^8
    • For the y terms: y^3 * y = y^(3+1) = y^4

  3. Combine the results: (2 * 3)(x^5 * x^3)(y^3 * y) = 6x^8y^4

Final Result

Therefore, the simplified expression is 6x^8y^4.

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