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Simplifying the Expression (-2x²y)(x³y²)³
This article will guide you through the process of simplifying the expression (-2x²y)(x³y²)³. We will break down each step and explain the rules used in simplification.
Understanding the Expression
The expression contains:
- Coefficients: -2
- Variables: x and y
- Exponents: 2, 3, and 3
Applying the Rules of Exponents
1. Power of a Product Rule: This rule states that (ab)ⁿ = aⁿbⁿ.
- Apply this to the term (x³y²)³: (x³y²)³ = (x³)^3 (y²)^3 = x⁹y⁶
2. Power of a Power Rule: This rule states that (aⁿ)ᵐ = aⁿᵐ.
- We can simplify x⁹y⁶ further by using this rule: x⁹y⁶ = (x¹⁸)(y⁶)
3. Multiplication of Monomials: When multiplying monomials, we multiply the coefficients and add the exponents of the same variables.
Simplifying the Expression
Now we can simplify the entire expression:
- (-2x²y)(x³y²)³ = (-2x²y)(x⁹y⁶)
- = -2 * x² * x⁹ * y * y⁶
- = -2x¹¹y⁷
Conclusion
Therefore, the simplified expression for (-2x²y)(x³y²)³ is -2x¹¹y⁷. By applying the rules of exponents and simplifying step by step, we arrive at the final answer.