Question

simplify.
$(-2y^{3}z^{2})^{4}(2x^{2}y^{4}z)$

Explanation:

Step1: Simplify \((-2y^{3}z^{2})^{4}\)

Using the power of a product rule \((ab)^n = a^n b^n\) and \((a^m)^n=a^{mn}\), we have:
\((-2)^4(y^{3})^{4}(z^{2})^{4}=16y^{12}z^{8}\)

Step2: Simplify \((2x^{2}y^{4}z)\)

This term is already in a relatively simple form, but we will multiply it with the result from Step 1.

Step3: Multiply the two simplified terms

Multiply \(16y^{12}z^{8}\) and \(2x^{2}y^{4}z\) using the product rule for exponents \(a^m \cdot a^n = a^{m + n}\) and the commutative property of multiplication:
\((16\times2)x^{2}(y^{12}\cdot y^{4})(z^{8}\cdot z)=32x^{2}y^{16}z^{9}\)

Answer:

\(32x^{2}y^{16}z^{9}\)