Question

use the product rule to simplify. (-6x²)(-7x⁹)

Explanation:

Step1: Recall the product rule for exponents

The product rule for exponents states that \(a^m \cdot a^n = a^{m + n}\), and for multiplying coefficients, we multiply them as usual. Also, the product of two negative numbers is positive.
First, multiply the coefficients: \((-6)\times(-7)=42\)

Step2: Multiply the variables using the product rule

For the variables \(x^2\) and \(x^9\), using the product rule \(x^2\cdot x^9 = x^{2 + 9}=x^{11}\)

Step3: Combine the results

Multiply the result of the coefficients and the result of the variables together: \(42\times x^{11}=42x^{11}\)

Answer:

\(42x^{11}\)