Question

use the product rule to simplify the expression. write the re
(6z^{10})(-2z^{6})(z^{3})
(6z^{10})(-2z^{6})(z^{3}) = \square

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(6 \times (-2) \times 1 = -12\)

Step2: Apply the product rule for exponents

For the variable \(z\), use the product rule \(a^m \times a^n = a^{m + n}\). So \(z^{10} \times z^6 \times z^3 = z^{10 + 6 + 3} = z^{19}\)

Step3: Combine the results

Multiply the coefficient and the variable part together: \(-12 \times z^{19} = -12z^{19}\)

Answer:

\(-12z^{19}\)