Question

simplify.
\\((-2x^{3}yz^{3})(3x^{3}y^{2}z)^{3}\\)

Explanation:

Step1: Simplify the power of the second term

First, we apply the power of a product rule \((ab)^n = a^n b^n\) and the power of a power rule \((a^m)^n=a^{mn}\) to \((3x^{3}y^{2}z)^{3}\).

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Step2: Multiply the two monomials

Now we multiply \((-2x^{3}yz^{3})\) with \(27x^{9}y^{6}z^{3}\). We use the product rule for exponents \(a^{m}\cdot a^{n}=a^{m + n}\) for the same base.

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Answer:

\(-54x^{12}y^{7}z^{6}\)