(3x^4y^-2)(2x^5y^4z^0)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (3x⁴y⁻²) (2x⁵y⁴z⁰)

This article explores the simplification of the algebraic expression (3x⁴y⁻²) (2x⁵y⁴z⁰). We will utilize the rules of exponents to achieve a concise and simplified form.

Understanding the Rules of Exponents

Before we embark on simplifying the expression, let's review the relevant rules of exponents:

• Product of powers: When multiplying powers with the same base, add the exponents. xᵃ ⋅ xᵇ = xᵃ⁺ᵇ
• Quotient of powers: When dividing powers with the same base, subtract the exponents. xᵃ / xᵇ = xᵃ⁻ᵇ
• Power of a power: When raising a power to another power, multiply the exponents. (xᵃ)ᵇ = xᵃᵇ
• Zero exponent: Any non-zero number raised to the power of zero equals one. x⁰ = 1

Simplifying the Expression

1. Apply the product of powers rule:

   • (3x⁴y⁻²) (2x⁵y⁴z⁰) = 3 * 2 * x⁴⁺⁵ * y⁻²⁺⁴ * z⁰

2. Simplify the coefficients and exponents:

   • 6x⁹y²z⁰

3. Apply the zero exponent rule:

   • 6x⁹y² * 1

4. Final simplified form:

   • 6x⁹y²

Therefore, the simplified form of the expression (3x⁴y⁻²) (2x⁵y⁴z⁰) is 6x⁹y².