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Simplifying Expressions with Exponents: (3xy⁴)²(y²)³
In algebra, simplifying expressions involving exponents is a crucial skill. Let's break down how to simplify the expression (3xy⁴)²(y²)³.
Understanding the Rules of Exponents
- Product of powers: When multiplying powers with the same base, add the exponents. For example, xᵃ * xᵇ = xᵃ⁺ᵇ.
- Power of a product: When raising a product to a power, raise each factor to that power. For example, (xy)ᵃ = xᵃyᵃ.
- Power of a power: When raising a power to another power, multiply the exponents. For example, (xᵃ)ᵇ = xᵃᵇ.
Simplifying the Expression
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Apply the power of a product rule: (3xy⁴)² = 3² * x² * (y⁴)² = 9x²y⁸
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Apply the power of a power rule: (y²)³ = y⁶
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Now we have: 9x²y⁸ * y⁶
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Apply the product of powers rule: 9x²y⁸ * y⁶ = 9x²y¹⁴
Final Result
Therefore, the simplified form of (3xy⁴)²(y²)³ is 9x²y¹⁴.