%5E2.jpeg "(3xy^4x^2y)^2")
Simplifying the Expression (3xy^4x^2y)^2
This article will guide you through the process of simplifying the expression (3xy^4x^2y)^2.
Understanding the Expression
The expression involves:
- Coefficients: The number 3.
- Variables: x and y, with exponents.
- Exponents: The power of 2 outside the parentheses.
Applying the Rules of Exponents
To simplify the expression, we'll utilize the following rules of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Simplifying the Expression
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Apply the power of a product rule: (3xy^4x^2y)^2 = 3^2 * (x)^2 * (y^4)^2 * (x^2)^2 * (y)^2
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Simplify the exponents: 3^2 * (x)^2 * (y^4)^2 * (x^2)^2 * (y)^2 = 9 * x^2 * y^8 * x^4 * y^2
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Combine like terms: 9 * x^2 * y^8 * x^4 * y^2 = 9 * x^(2+4) * y^(8+2)
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Final simplified form: 9 * x^(2+4) * y^(8+2) = 9x^6y^10
Conclusion
Therefore, the simplified form of the expression (3xy^4x^2y)^2 is 9x^6y^10. Remember to apply the rules of exponents correctly and systematically to simplify such expressions.