Question

1. \\(\frac{4x^{2}z^{0}}{2x^{3}z}\\)

Explanation:

Step1: Simplify coefficients

Simplify the coefficient fraction $\frac{4}{2}$.
$\frac{4}{2} = 2$

Step2: Simplify \(x\)-terms

Use the rule of exponents $\frac{x^m}{x^n}=x^{m - n}$ for \(x\)-terms. Here, \(m = 2\), \(n = 3\).
$\frac{x^{2}}{x^{3}}=x^{2 - 3}=x^{-1}=\frac{1}{x}$

Step3: Simplify \(z\)-terms

Use the rule of exponents $\frac{z^m}{z^n}=z^{m - n}$ for \(z\)-terms. Recall that \(z^0 = 1\), so \(m = 0\), \(n = 1\).
$\frac{z^{0}}{z^{1}}=z^{0 - 1}=z^{-1}=\frac{1}{z}$

Step4: Combine all parts

Multiply the simplified coefficient, \(x\)-term, and \(z\)-term together.
$2\times\frac{1}{x}\times\frac{1}{z}=\frac{2}{xz}$

Answer:

$\frac{2}{xz}$