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

Question

Accepted Answer

# 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:
$18x^{8}y^{5}z^{5}$

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QUESTION IMAGE

Question

Explanation:

Step1: Apply power of a product rule

Step2: Multiply with the second term

Answer: