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Simplifying the Expression: (2x²y)³(3x²y³)
This article will guide you through simplifying the expression **(2x²y)³(3x²y³) **using the rules of exponents.
Understanding the Rules
To simplify this expression, we need to recall the following rules of exponents:
- Power of a product: (ab)ⁿ = aⁿbⁿ
- Power of a power: (aⁿ)ᵐ = aⁿᵐ
- Product of powers: aⁿaᵐ = aⁿ⁺ᵐ
Applying the Rules
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Simplify (2x²y)³:
- Apply the power of a product rule: (2x²y)³ = 2³(x²)³y³
- Apply the power of a power rule: 2³(x²)³y³ = 8x⁶y³
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Combine the simplified terms:
- Now we have: 8x⁶y³ * 3x²y³
- Apply the product of powers rule: 8x⁶y³ * 3x²y³ = 24x⁸y⁶
Final Answer
Therefore, the simplified form of **(2x²y)³(3x²y³) **is 24x⁸y⁶.