[tex]\dfrac{3xyz^2}{6y^4}=\dfrac{3}{6}\cdot\dfrac{xyz^2}{y^4}=\dfrac{1}{2}\cdot\dfrac{xz}{y^3}=\dfrac{xz}{2y^3}\\\\\\\dfrac{3xyz^2}{6y^4}\cdot\dfrac{2y}{xz^4}=\dfrac{xz^2}{2y^3}\cdot\dfrac{2y}{xz^4}=\dfrac{2}{2}\cdot\dfrac{xyz^2}{xy^3z^4}=1\cdot\dfrac{1}{y^2z^2}=\dfrac{1}{y^2z^2}[/tex]
The product of the expression is:
[tex]\dfrac{1}{y^2z^2}[/tex]
We are asked to multiply the expression:
[tex]\dfrac{3xyz^2}{6y^4}\times \dfrac{2y}{xz^4}[/tex]
i.e.
The numerator terms get multiplied to each other and the denominator terms get multiplied to each other
i.e. we may write the expression as follows:
[tex]=\dfrac{(3xyz^2)\cdot (2y)}{(6y^4)\cdot (xz^4)}\\\\\\=\dfrac{6xy^2z^2}{6xy^4z^4}\\\\=\dfrac{6}{6}\times \dfrac{x}{x}\times \dfrac{y^2}{y^4}\times \dfrac{z^2}{z^4}\\\\=y^{2-4}\times z^{2-4}\\\\=y^{-2}\times z^{-2}\\\\i.e.\\\\=\dfrac{1}{y^2}\times \dfrac{1}{z^2}\\\\=\dfrac{1}{y^2z^2}[/tex]
