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Simplifying (3x⁴y⁵)³
This expression involves exponents and parentheses. To simplify it, we'll use the following rules:
1. Power of a Product: (ab)ⁿ = aⁿbⁿ 2. Power of a Power: (aⁿ)ᵐ = aⁿᵐ
Step-by-step solution:
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Apply the power of a product rule: (3x⁴y⁵)³ = 3³(x⁴)³(y⁵)³
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Apply the power of a power rule: 3³(x⁴)³(y⁵)³ = 27x¹²y¹⁵
Therefore, the simplified form of (3x⁴y⁵)³ is 27x¹²y¹⁵.
Explanation:
- We cube each factor inside the parentheses.
- We multiply the exponents of each variable by the power outside the parentheses.
This simplified form is useful for calculations, algebraic manipulations, and understanding the relationship between the original expression and its simplified equivalent.