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Simplifying Expressions: (7xy²)(2x⁴y³)
In mathematics, simplifying expressions often involves combining like terms and applying the rules of exponents. Let's break down the process of simplifying the expression **(7xy²)(2x⁴y³) **
Understanding the Rules
- Multiplication of Variables: When multiplying variables with the same base, add their exponents. For example, x² * x³ = x⁵.
- Multiplication of Coefficients: Treat the coefficients like regular numbers and multiply them together.
Step-by-Step Simplification
- Multiply the coefficients: 7 * 2 = 14
- Combine the 'x' terms: x¹ * x⁴ = x⁵ (Remember that x has an implicit exponent of 1)
- Combine the 'y' terms: y² * y³ = y⁵
The Simplified Expression
By combining the steps above, we arrive at the simplified form:
(7xy²)(2x⁴y³) = 14x⁵y⁵
Conclusion
Simplifying expressions like (7xy²)(2x⁴y³) involves applying basic rules of exponents and multiplication. This process can be broken down into smaller, manageable steps to ensure accuracy and understanding.