%5E5.jpeg "(3x^4y^2)^5")
Simplifying the Expression (3x⁴y²)⁵
In this article, we will explore how to simplify the expression (3x⁴y²)⁵. This involves understanding the rules of exponents and applying them to the given expression.
Understanding the Rules of Exponents
The key to simplifying this expression lies in understanding the following rules of exponents:
- Product of powers: (a^m)^n = a^(m*n)
- Power of a product: (ab)^n = a^n * b^n
Simplifying the Expression
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Applying the power of a product rule: We begin by applying the power of a product rule to the expression: (3x⁴y²)⁵ = 3⁵ * (x⁴)⁵ * (y²)⁵
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Applying the product of powers rule: Next, we apply the product of powers rule to each term: 3⁵ * (x⁴)⁵ * (y²)⁵ = 3⁵ * x^(45) * y^(25)
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Simplifying the exponents: Finally, we simplify the exponents: 3⁵ * x^(45) * y^(25) = 243x²⁰y¹⁰
Conclusion
Therefore, the simplified form of the expression (3x⁴y²)⁵ is 243x²⁰y¹⁰. By understanding the rules of exponents, we can effectively simplify complex expressions and arrive at a concise and manageable solution.