(-2x%5E3y).jpeg "(-3xy^3)(-2x^3y)")
Simplifying the Expression (-3xy^3)(-2x^3y)
This article will demonstrate how to simplify the expression (-3xy^3)(-2x^3y). We'll break down the process step by step for clarity.
Understanding the Basics
The expression involves multiplication of monomials, which are algebraic expressions with a single term. Each monomial consists of a coefficient (a numerical value) and one or more variables raised to powers.
Applying the Laws of Exponents
The key to simplifying this expression lies in applying the laws of exponents, specifically:
- Product of Powers: When multiplying powers with the same base, add the exponents.
- x^m * x^n = x^(m+n)
Step-by-Step Solution
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Rearrange the terms: Group the coefficients and the variables separately. (-3xy^3)(-2x^3y) = (-3)(-2) * (x)(x^3) * (y^3)(y)
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Multiply the coefficients: (-3)(-2) * (x)(x^3) * (y^3)(y) = 6 * (x)(x^3) * (y^3)(y)
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Apply the product of powers rule for variables: 6 * (x)(x^3) * (y^3)(y) = 6 * x^(1+3) * y^(3+1)
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Simplify: 6 * x^(1+3) * y^(3+1) = 6x^4y^4
Conclusion
Therefore, the simplified expression for (-3xy^3)(-2x^3y) is 6x^4y^4. This process illustrates the importance of understanding the basic laws of exponents in simplifying algebraic expressions.