%5E4.jpeg "(3x^5y)^4")
Simplifying (3x^5y)^4
In mathematics, simplifying expressions often involves applying the rules of exponents. In this case, we have the expression (3x^5y)^4. Let's break down how to simplify it:
Understanding the 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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Apply the Power of a Product Rule: (3x^5y)^4 = 3^4 * (x^5)^4 * y^4
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Apply the Product of Powers Rule: 3^4 * (x^5)^4 * y^4 = 81 * x^(5*4) * y^4
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Simplify: 81 * x^(5*4) * y^4 = 81x^20y^4
Therefore, the simplified form of (3x^5y)^4 is 81x^20y^4.
Key Takeaways
- Understanding the rules of exponents is crucial for simplifying expressions.
- By applying these rules step by step, we can simplify complex expressions into their simplest forms.
- The simplified expression 81x^20y^4 represents the same value as the original expression (3x^5y)^4.