%5E3.jpeg "(4x^3y^5)^3")
Simplifying the Expression (4x^3y^5)^3
In mathematics, we often encounter expressions with exponents and variables. Simplifying these expressions involves understanding the rules of exponents and applying them correctly. Let's explore how to simplify the expression (4x^3y^5)^3.
Understanding the Properties of Exponents
The key to simplifying this expression lies in the following 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 to Simplify
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Apply the power of a product property: (4x^3y^5)^3 = 4^3 * (x^3)^3 * (y^5)^3
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Apply the power of a power property: 4^3 * (x^3)^3 * (y^5)^3 = 64 * x^(33) * y^(53)
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Simplify the exponents: 64 * x^(33) * y^(53) = 64x^9y^15
Final Result
Therefore, the simplified form of (4x^3y^5)^3 is 64x^9y^15.
Conclusion
By understanding the properties of exponents and applying them systematically, we can simplify complex expressions like (4x^3y^5)^3. This process is essential for solving equations, manipulating algebraic expressions, and understanding various mathematical concepts.