%5E2.jpeg "(-4x^5y^2)^2")
Simplifying (-4x^5y^2)^2
In mathematics, simplifying expressions often involves applying rules of exponents. Let's break down how to simplify the expression (-4x^5y^2)^2.
Understanding the Properties of Exponents
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Properties to the Expression
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Apply the Power of a Product property: (-4x^5y^2)^2 = (-4)^2 * (x^5)^2 * (y^2)^2
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Apply the Power of a Power property: (-4)^2 * (x^5)^2 * (y^2)^2 = 16 * x^(52) * y^(22)
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Simplify the exponents: 16 * x^(52) * y^(22) = 16x^10y^4
Final Result
Therefore, the simplified form of (-4x^5y^2)^2 is 16x^10y^4.