(-2xy)%5E3.jpeg "(3x^2y)(-2xy)^3")
Simplifying Algebraic Expressions: (3x²y)(-2xy)³
This article will guide you through simplifying the algebraic expression (3x²y)(-2xy)³.
Understanding the Expression
The expression involves multiplication of monomials. Here's a breakdown:
- (3x²y): This is a monomial with a coefficient of 3 and variables x² and y.
- (-2xy)³: This represents the monomial (-2xy) multiplied by itself three times.
Applying the Rules of Exponents
To simplify the expression, we need to apply the following rules of exponents:
- Product of Powers: When multiplying powers with the same base, add the exponents. (x^m * x^n = x^(m+n))
- Power of a Product: When raising a product to a power, raise each factor to that power. [(xy)^n = x^n * y^n]
- Power of a Power: When raising a power to another power, multiply the exponents. [(x^m)^n = x^(m*n)]
Simplifying the Expression
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Simplify (-2xy)³:
- (-2xy)³ = (-2)³ * x³ * y³ = -8x³y³
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Multiply the simplified terms:
- (3x²y)(-8x³y³) = 3 * -8 * x² * x³ * y * y³
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Apply the Product of Powers Rule:
- -24 * x^(2+3) * y^(1+3)
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Simplify:
- -24x⁵y⁴
Conclusion
Therefore, the simplified form of the algebraic expression (3x²y)(-2xy)³ is -24x⁵y⁴. Remember to carefully apply the rules of exponents when simplifying algebraic expressions involving powers and multiplications.