(4ab^3)(-5b^6)(2a^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (4ab^3)(-5b^6)(2a^2).

Understanding the Properties of Exponents

Before we begin, let's refresh our memory on the properties of exponents that will be crucial in simplifying our expression:

• Product of powers: x^m * x^n = x^(m+n)
• Commutative Property: a * b = b * a

Step-by-Step Simplification

1. Rearrange the terms: Using the commutative property, we can rearrange the terms to group the coefficients and variables with the same base together.

   (4ab^3)(-5b^6)(2a^2) = (4 * -5 * 2) * (a * a^2) * (b^3 * b^6)

2. Multiply the coefficients: (4 * -5 * 2) * (a * a^2) * (b^3 * b^6) = -40 * (a * a^2) * (b^3 * b^6)

3. Apply the product of powers rule: -40 * (a * a^2) * (b^3 * b^6) = -40 * a^(1+2) * b^(3+6)

4. Simplify: -40 * a^(1+2) * b^(3+6) = -40a^3b^9

Conclusion

Therefore, the simplified form of the expression (4ab^3)(-5b^6)(2a^2) is -40a^3b^9. By understanding the properties of exponents and applying them step-by-step, we can efficiently simplify complex expressions.