(6xy%5E5).jpeg "(3x^2y^3)(6xy^5)")
Simplifying Algebraic Expressions: (3x²y³)(6xy⁵)
This article will walk you through the process of simplifying the algebraic expression (3x²y³)(6xy⁵).
Understanding the Basics
Before we begin, let's review a few key concepts:
- Coefficients: Numbers that multiply variables (e.g., 3 in 3x²y³)
- Variables: Letters representing unknown values (e.g., x and y)
- Exponents: Small numbers written above and to the right of a variable indicating repeated multiplication (e.g., ² in x² means x * x)
Simplifying the Expression
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Identify the coefficients and variables:
- Coefficients: 3 and 6
- Variables: x and y
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Multiply the coefficients: 3 * 6 = 18
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Combine the 'x' variables: x² * x = x^(2+1) = x³ (Remember: when multiplying variables with exponents, add the exponents)
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Combine the 'y' variables: y³ * y⁵ = y^(3+5) = y⁸
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Combine the results: 18x³y⁸
Final Answer
The simplified form of the expression (3x²y³)(6xy⁵) is 18x³y⁸.