%5E2%2F4x%5E2y%5E5.jpeg "(6x^2y^3)^2/4x^2y^5")
Simplifying Algebraic Expressions: (6x²y³)² / 4x²y⁵
This article will guide you through simplifying the algebraic expression (6x²y³)² / 4x²y⁵.
Understanding the Expression
The expression (6x²y³)² / 4x²y⁵ involves several key mathematical concepts:
- Exponents: The small numbers written above the variables (like the "2" in x²) indicate repeated multiplication.
- Parentheses: The parentheses indicate that the entire expression inside needs to be squared first.
- Fractions: The line between the expressions signifies division.
Simplifying the Expression
Let's break down the simplification step by step:
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Square the numerator: (6x²y³)² means multiplying the entire expression by itself: (6x²y³) * (6x²y³) = 36x⁴y⁶
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Rewrite the expression: Now the expression becomes: 36x⁴y⁶ / 4x²y⁵
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Simplify by dividing: To simplify, we can divide the coefficients (36 and 4) and the variables with the same base.
- 36 / 4 = 9
- x⁴ / x² = x² (subtract the exponents when dividing variables with the same base)
- y⁶ / y⁵ = y (subtract the exponents)
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Final result: The simplified expression is 9x²y.
Conclusion
By understanding the rules of exponents, parentheses, and division, we can simplify complex algebraic expressions like (6x²y³)² / 4x²y⁵. The simplified expression 9x²y is equivalent to the original expression but in a more concise form.