%5E2.jpeg "(2x^3y^3)^2")
Simplifying (2x^3y^3)^2
This article will explore the simplification of the expression (2x^3y^3)^2. We will break down the process step-by-step, using the rules of exponents.
Understanding the Rules
Before we start, let's review a few key exponent rules:
- Product of powers: (x^m) * (x^n) = x^(m+n)
- Power of a power: (x^m)^n = x^(m*n)
- Power of a product: (xy)^n = x^n * y^n
Simplifying the Expression
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Apply the power of a product rule: (2x^3y^3)^2 = 2^2 * (x^3)^2 * (y^3)^2
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Apply the power of a power rule: 2^2 * (x^3)^2 * (y^3)^2 = 4 * x^(32) * y^(32)
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Simplify the exponents: 4 * x^(32) * y^(32) = 4x^6y^6
Final Result
Therefore, the simplified form of (2x^3y^3)^2 is 4x^6y^6.
Conclusion
By applying the fundamental rules of exponents, we successfully simplified the given expression. This process highlights the importance of understanding and applying these rules effectively in algebraic manipulations.