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Simplifying Expressions with Exponents: (x^2y^4)^5
This article will guide you through simplifying the expression (x^2y^4)^5.
Understanding the Rules of Exponents
When dealing with exponents, we need to remember a few key rules:
- Product of Powers: When multiplying powers with the same base, we add their exponents: x^m * x^n = x^(m+n)
- Power of a Power: When raising a power to another power, we multiply their exponents: (x^m)^n = x^(m*n)
- Power of a Product: When raising a product to a power, we raise each factor to that power: (xy)^n = x^n * y^n
Simplifying the Expression
Let's break down the simplification of (x^2y^4)^5 step by step:
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Apply the Power of a Power Rule: We have a power raised to another power. Therefore, we multiply the exponents: (x^2y^4)^5 = x^(25) * y^(45)
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Simplify the Exponents: x^(25) * y^(45) = x^10 * y^20
Final Result
The simplified form of the expression (x^2y^4)^5 is x^10y^20.
Conclusion
Understanding the rules of exponents allows us to effectively simplify complex expressions. By applying these rules, we can express the given expression in a concise and manageable form.