%5E3.jpeg "(4x^2y^3)^3")
Simplifying the Expression (4x^2y^3)^3
This article will guide you through the process of simplifying the expression (4x^2y^3)^3.
Understanding the Properties of Exponents
To simplify this expression, we need to recall some key properties of exponents:
- Power of a Product: (ab)^n = a^n * b^n
- Power of a Power: (a^m)^n = a^(m*n)
Applying the Properties
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Distributing the exponent: Using the power of a product property, we can rewrite the expression as: (4^3) * (x^2)^3 * (y^3)^3
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Simplifying exponents: Now, applying the power of a power property, we get: 64 * x^(23) * y^(33)
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Final Simplification: This simplifies to 64x^6y^9
Conclusion
Therefore, the simplified form of the expression (4x^2y^3)^3 is 64x^6y^9. Remember, understanding the properties of exponents is crucial for simplifying expressions and solving complex equations.