Question

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

Explanation:

Step1: Apply power of a product rule

For \((-y^{2}z^{4})^{3}\), using \((ab)^n=a^n b^n\) and \((a^m)^n=a^{mn}\), we get \((-1)^3(y^{2})^{3}(z^{4})^{3}=-1\times y^{6}\times z^{12}=-y^{6}z^{12}\).
For \((-x^{3}z^{3})^{2}\), using the same rules, we get \((-1)^2(x^{3})^{2}(z^{3})^{2}=1\times x^{6}\times z^{6}=x^{6}z^{6}\).

Step2: Multiply the two results

Multiply \(-y^{6}z^{12}\) and \(x^{6}z^{6}\) using \(a^m\times a^n=a^{m + n}\) for the \(z\) terms: \(-y^{6}z^{12}\times x^{6}z^{6}=-x^{6}y^{6}z^{12 + 6}=-x^{6}y^{6}z^{18}\).

Answer:

\(-x^{6}y^{6}z^{18}\)