(3x%5E5y)%5E2.jpeg "(4x^3y^5)(3x^5y)^2")
Simplifying the Expression (4x^3y^5)(3x^5y)^2
This article will guide you through the process of simplifying the expression (4x^3y^5)(3x^5y)^2. We will utilize the rules of exponents and algebraic manipulations to achieve a concise and simplified form.
Understanding the Rules of Exponents
Before we begin, let's recall the essential rules of exponents that we will be using:
- Product of Powers: x^m * x^n = x^(m+n)
- Power of a Product: (xy)^n = x^n * y^n
- Power of a Power: (x^m)^n = x^(m*n)
Simplifying the Expression
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Apply the Power of a Product Rule: (3x^5y)^2 = 3^2 * (x^5)^2 * y^2 = 9x^10y^2
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Rewrite the Expression: The original expression now becomes: (4x^3y^5)(9x^10y^2)
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Apply the Product of Powers Rule: Multiply the coefficients: 4 * 9 = 36 Multiply the x terms: x^3 * x^10 = x^(3+10) = x^13 Multiply the y terms: y^5 * y^2 = y^(5+2) = y^7
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Final Simplified Expression: The simplified form of the expression is 36x^13y^7.
Conclusion
By applying the rules of exponents, we successfully simplified the expression (4x^3y^5)(3x^5y)^2 to 36x^13y^7. This process demonstrates the importance of understanding and applying these rules in algebraic manipulations.