%5E2.jpeg "(4xy^2)^2")
Simplifying the Expression (4xy^2)^2
The expression (4xy^2)^2 represents the square of a monomial. To simplify this, we need to apply the rules of exponents.
Understanding the Rules of Exponents
The key principle here is that when raising a product to a power, we raise each factor in the product to that power. In other words:
(ab)^n = a^n * b^n
Applying the Rules
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Identify the factors: Our factors are 4, x, and y^2.
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Apply the power to each factor:
- 4^2 = 16
- x^2 = x^2
- (y^2)^2 = y^(2*2) = y^4
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Combine the simplified factors: 16 * x^2 * y^4
Final Result
Therefore, (4xy^2)^2 simplifies to 16x^2y^4.