%5E2.jpeg "(3xy^4/5z^2)^2")
Simplifying Expressions with Exponents: (3xy^4/5z^2)^2
This article will guide you through the process of simplifying the expression (3xy^4/5z^2)^2. We'll break down the steps involved in applying the rules of exponents to achieve a simplified form.
Understanding the Rules
Before we dive into the simplification, let's review the key exponent rules that we'll be using:
- Product of Powers: (a^m)(a^n) = a^(m+n)
- Power of a Quotient: (a/b)^n = a^n / b^n
- Power of a Product: (ab)^n = a^n b^n
- Power of a Power: (a^m)^n = a^(m*n)
Simplifying the Expression
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Apply the Power of a Quotient rule: (3xy^4/5z^2)^2 = (3xy^4)^2 / (5z^2)^2
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Apply the Power of a Product rule to both the numerator and denominator: = (3^2 x^2 y^(42)) / (5^2 z^(22))
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Simplify by multiplying the exponents: = 9x^2 y^8 / 25z^4
Final Result
Therefore, the simplified form of (3xy^4/5z^2)^2 is 9x^2 y^8 / 25z^4.
Key Takeaways
By understanding the rules of exponents and applying them systematically, you can efficiently simplify complex expressions like this one. Remember to break down the problem into smaller steps and carefully track the application of each rule.