%5E4.jpeg "(2xy^3)^4")
Simplifying (2xy^3)^4
In mathematics, simplifying expressions is a key skill. This article will guide you through the process of simplifying the expression (2xy^3)^4.
Understanding the Power of a Product Rule
The expression involves raising a product (2xy^3) to a power (4). This requires us to apply the power of a product rule:
(ab)^n = a^n * b^n
Where 'a' and 'b' are any numbers or variables, and 'n' is an integer.
Applying the Rule
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Apply the power of a product rule: (2xy^3)^4 = 2^4 * x^4 * (y^3)^4
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Simplify each term:
- 2^4 = 16
- x^4 = x^4
- (y^3)^4 = y^(3*4) = y^12
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Combine the simplified terms: 16 * x^4 * y^12 = 16x^4y^12
Conclusion
Therefore, the simplified form of (2xy^3)^4 is 16x^4y^12. This demonstrates the importance of applying the appropriate rules of exponents to simplify complex expressions.