Question

(\frac{2x^{4}y^{-4}z^{-3}}{3x^{2}y^{-3}z^{4}})

Explanation:

Step1: Separate coefficient and variables

$\frac{2}{3} \cdot \frac{x^4}{x^2} \cdot \frac{y^{-4}}{y^{-3}} \cdot \frac{z^{-3}}{z^4}$

Step2: Simplify $x$-terms (subtract exponents)

$\frac{x^4}{x^2}=x^{4-2}=x^2$

Step3: Simplify $y$-terms (subtract exponents)

$\frac{y^{-4}}{y^{-3}}=y^{-4-(-3)}=y^{-1}=\frac{1}{y}$

Step4: Simplify $z$-terms (subtract exponents)

$\frac{z^{-3}}{z^4}=z^{-3-4}=z^{-7}=\frac{1}{z^7}$

Step5: Combine all simplified parts

$\frac{2}{3} \cdot x^2 \cdot \frac{1}{y} \cdot \frac{1}{z^7}$

Answer:

$\frac{2x^2}{3yz^7}$