Question

use the product rule to simplify the expression. write the result using exponents.\\((-2y^{2}z^{6})(9yz^{2})\\)\\((-2y^{2}z^{6})(9yz^{2})=\square\\)

Explanation:

Step1: Multiply the coefficients

Multiply -2 and 9: $-2\times9 = -18$

Step2: Multiply the y terms

Use the product rule $a^m\times a^n = a^{m + n}$ for $y^2$ and $y$ (which is $y^1$): $y^2\times y^1 = y^{2 + 1}=y^3$

Step3: Multiply the z terms

Use the product rule for $z^6$ and $z^2$: $z^6\times z^2 = z^{6 + 2}=z^8$

Step4: Combine all parts

Multiply the results from Step1, Step2, and Step3: $-18\times y^3\times z^8=-18y^3z^8$

Answer:

$-18y^3z^8$