(4x^2y^5)^-2

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Negative Exponents: (4x²y⁵)⁻²

In mathematics, negative exponents indicate the reciprocal of a base raised to the corresponding positive exponent. This concept is crucial for simplifying expressions involving negative exponents. Let's explore how to simplify the expression (4x²y⁵)⁻².

Understanding the Rules

1. Reciprocal: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. In our case, (4x²y⁵)⁻² becomes 1/(4x²y⁵)².

2. Power of a product: When a product is raised to a power, each factor within the product is raised to that power. Therefore, (4x²y⁵)² becomes 4² * (x²)² * (y⁵)².

Simplifying the Expression

1. Applying the reciprocal rule: (4x²y⁵)⁻² = 1/(4x²y⁵)²

2. Applying the power of a product rule: 1/(4² * (x²)² * (y⁵)²)

3. Simplifying: 1/(16x⁴y¹⁰)

Final Result

Therefore, the simplified form of (4x²y⁵)⁻² is 1/(16x⁴y¹⁰).