Question

simplify.
$\left(-3x^{4}y^{2}z\
ight)^{2}\left(2yz^{3}\
ight)$

Explanation:

Step1: Apply power of a product rule

First, apply the power of a product rule \((ab)^n = a^n b^n\) to \((-3x^{4}y^{2}z)^{2}\).
\[

$$\begin{align*} (-3x^{4}y^{2}z)^{2}&=(-3)^{2}(x^{4})^{2}(y^{2})^{2}(z)^{2}\\ &=9x^{8}y^{4}z^{2} \end{align*}$$

\]

Step2: Multiply with the second term

Now, multiply the result from Step 1 with \(2yz^{3}\). When multiplying terms with the same base, we add the exponents.
\[

$$\begin{align*} 9x^{8}y^{4}z^{2}\cdot2yz^{3}&=(9\times2)x^{8}(y^{4}\cdot y)(z^{2}\cdot z^{3})\\ &=18x^{8}y^{4 + 1}z^{2+3}\\ &=18x^{8}y^{5}z^{5} \end{align*}$$

\]

Answer:

\(18x^{8}y^{5}z^{5}\)