(-3ab^4)(4ab^-3)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-3ab^4)(4ab^-3)

This article will guide you through simplifying the expression (-3ab^4)(4ab^-3). We'll break down the steps involved in simplifying this expression using the rules of exponents.

Understanding the Rules of Exponents

Before diving into the simplification, let's recall the key rules of exponents that we'll use:

• Product of Powers: When multiplying powers with the same base, we add the exponents: x^m * x^n = x^(m+n)
• Negative Exponent: Any base raised to a negative exponent is equal to its reciprocal raised to the positive exponent: x^-n = 1/x^n

Simplifying the Expression

1. Combine the coefficients: Multiply the numerical coefficients: (-3) * (4) = -12

2. Apply the Product of Powers rule for 'a': a^1 * a^1 = a^(1+1) = a^2

3. Apply the Product of Powers rule for 'b': b^4 * b^-3 = b^(4-3) = b^1 = b

4. Combine the results: (-12) * a^2 * b = -12a^2b

Final Answer

Therefore, the simplified expression of (-3ab^4)(4ab^-3) is -12a^2b.