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5.1: Правила експонентів
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\(\begin{aligned} \left( \frac{-2x^{3}y^{4}z}{xy^{2}} \right)^{4}&=(-2\cdot x^{3-1}\cdot y^{4-2}\cdot z)^{4} &\color{Cerulean}{Simplify\:within\:the\:parentheses\:first.} \\ &=(-2\cdot x^{2}\cdot y^{2... $\begin{aligned} \left( \frac{-2x^{3}y^{4}z}{xy^{2}} \right)^{4}&=(-2\cdot x^{3-1}\cdot y^{4-2}\cdot z)^{4} &\color{Cerulean}{Simplify\:within\:the\:parentheses\:first.} \\ &=(-2\cdot x^{2}\cdot y^{2} \cdot z)^{4} &\color{Cerulean}{Apply\:the\:power\:rule\:for\:a\:product.} \\ &=(-2)^{4}\cdot (x^{2})^{^{4}}\cdot (y^{2})^{^{4}}\cdot z^{4}&\color{Cerulean}{Apply\:the\:power\:rule\:for\:exponents.} \\ &=16x^{8}y^{8}z^{4} \end{aligned}$