(-4ab^3)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (-4ab^3)^2

In mathematics, simplifying expressions often involves applying the rules of exponents. Let's break down how to simplify the expression (-4ab^3)^2.

Understanding the Rules

• Power of a Product: (xy)^n = x^n * y^n
• Power of a Power: (x^m)^n = x^(m*n)

Applying the Rules

1. Apply the Power of a Product rule: (-4ab^3)^2 = (-4)^2 * a^2 * (b^3)^2

2. Apply the Power of a Power rule: (-4)^2 * a^2 * (b^3)^2 = 16 * a^2 * b^(3*2)

3. Simplify: 16 * a^2 * b^(3*2) = 16a^2b^6

Conclusion

Therefore, the simplified form of (-4ab^3)^2 is 16a^2b^6. This process involves applying the fundamental rules of exponents to break down the expression and reach the final simplified form.