%5E4.jpeg "(5x^3y/20xy^5)^4")
Simplifying the Expression: (5x^3y/20xy^5)^4
This article will guide you through the process of simplifying the expression (5x^3y/20xy^5)^4.
Understanding the Properties of Exponents
Before we begin, let's review some key properties of exponents:
- Product of powers: (x^m) * (x^n) = x^(m+n)
- Quotient of powers: (x^m) / (x^n) = x^(m-n)
- Power of a power: (x^m)^n = x^(m*n)
- Power of a product: (xy)^n = x^n * y^n
- Power of a quotient: (x/y)^n = x^n / y^n
Simplifying the Expression
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Simplify the fraction inside the parentheses: (5x^3y/20xy^5) = (x^2)/(4y^4)
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Apply the power of a quotient rule: [(x^2)/(4y^4)]^4 = (x^2)^4 / (4y^4)^4
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Apply the power of a power rule: (x^2)^4 / (4y^4)^4 = x^(24) / (4^4 * y^(44))
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Simplify the exponents: x^8 / (256y^16)
Final Result
The simplified expression is x^8 / (256y^16).
Conclusion
By applying the properties of exponents, we successfully simplified the complex expression. Remember to focus on understanding the rules and practice applying them to various expressions.