%5E-2-simplified.jpeg "(4x^2y^5)^-2 Simplified")
Simplifying (4x²y⁵)⁻²
This expression involves simplifying a term raised to a negative exponent. Let's break down the process step-by-step:
Understanding the Rules
- Negative Exponents: A term raised to a negative exponent is equivalent to its reciprocal raised to the positive value of that exponent. In other words: x⁻ⁿ = 1/xⁿ
- Power of a Product: When a product is raised to a power, each factor within the product is raised to that power. In other words: (xy)ⁿ = xⁿyⁿ
- Power of a Power: When a power is raised to another power, the exponents are multiplied. In other words: (xⁿ)ᵐ = xⁿᵐ
Applying the Rules
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Reciprocal: Since the expression is raised to the power of -2, we take its reciprocal: (4x²y⁵)⁻² = 1/(4x²y⁵)²
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Power of a Product: Apply the power of a product rule to the denominator: 1/(4x²y⁵)² = 1/(4²x²²y⁵²)
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Power of a Power: Simplify the exponents in the denominator: 1/(4²x²²y⁵²) = 1/(16x⁴y¹⁰)
Final Result
Therefore, the simplified form of (4x²y⁵)⁻² is 1/(16x⁴y¹⁰).