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Simplifying Algebraic Expressions: (2x^5y^3)(3x^3y)
This article will guide you through simplifying the algebraic expression (2x^5y^3)(3x^3y).
Understanding the Basics
The expression involves multiplying two monomials. Monomials are algebraic expressions consisting of a single term, which is a product of variables and coefficients.
- Coefficients: Numbers that multiply the variables. In our expression, the coefficients are 2 and 3.
- Variables: Letters that represent unknown values. In our expression, the variables are x and y.
- Exponents: Small numbers written above and to the right of a variable, indicating how many times the variable is multiplied by itself. In our expression, we have x^5, y^3, x^3, and y.
Applying the Rules
To simplify the expression, we need to use the following rules of exponents:
- Product of Powers: When multiplying powers with the same base, add the exponents. For example, x^m * x^n = x^(m+n).
- Commutative Property: The order of multiplication does not change the result. For example, a * b = b * a.
Simplifying the Expression
- Multiply the coefficients: 2 * 3 = 6
- Multiply the variables with the same base: x^5 * x^3 = x^(5+3) = x^8
- Multiply the remaining variables: y^3 * y = y^(3+1) = y^4
Combining all the results, we get: (2x^5y^3)(3x^3y) = 6x^8y^4
Conclusion
Therefore, the simplified form of the algebraic expression (2x^5y^3)(3x^3y) is 6x^8y^4. By applying the basic rules of exponents, we can effectively simplify and manipulate algebraic expressions.