%5E3.jpeg "(4x^2y^4)^3")
Simplifying (4x^2y^4)^3
This article will explore the simplification of the expression (4x^2y^4)^3. We will utilize the rules of exponents to achieve a simplified form.
Understanding the Rules of Exponents
Before we dive into the simplification, let's refresh our memory on some key exponent rules:
- Product of powers: (a^m) * (a^n) = a^(m+n)
- 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: (4x^2y^4)^3 = 4^3 * (x^2)^3 * (y^4)^3
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Apply the Power of a power rule: 4^3 * (x^2)^3 * (y^4)^3 = 64 * x^(23) * y^(43)
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Simplify: 64 * x^(23) * y^(43) = 64x^6y^12
Conclusion
Therefore, the simplified form of (4x^2y^4)^3 is 64x^6y^12. By applying the rules of exponents, we were able to break down the expression and arrive at a concise and clear representation.