%5E2(2x%5E3y%5E4)%5E3.jpeg "(-3x^5y^3)^2(2x^3y^4)^3")
Simplifying Algebraic Expressions: (-3x^5y^3)^2(2x^3y^4)^3
This article will guide you through simplifying the algebraic expression (-3x^5y^3)^2(2x^3y^4)^3. We will use the rules of exponents to break down the problem and arrive at a simplified solution.
Understanding the Rules of Exponents
Before we begin, let's review the key exponent rules we'll 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^3)^2 = (-3)^2 * (x^5)^2 * (y^3)^2 = 9x^10y^6
- (2x^3y^4)^3 = 2^3 * (x^3)^3 * (y^4)^3 = 8x^9y^12
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Substitute the simplified terms back into the original expression:
- 9x^10y^6 * 8x^9y^12
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Apply the Product of Powers Rule:
- 9 * 8 * x^(10+9) * y^(6+12) = 72x^19y^18
Final Solution
The simplified form of the expression (-3x^5y^3)^2(2x^3y^4)^3 is 72x^19y^18.
Key Takeaways
This example demonstrates the importance of understanding and applying exponent rules for simplifying complex algebraic expressions. Remember to break down the expression step by step and apply the appropriate rules to reach a simplified form.