What is the order of reaction for the rate law $r = k [A]^{\frac{3}{2}} [B]^2$ ?

$A$ complex reaction takes place in $2$ steps:
$(I)$ $NO_{2(g)} + F_{2(g)} \rightarrow NO_2F_{(g)} + F_{(g)}$ (slow)
$(II)$ $F_{(g)} + NO_{2(g)} \rightarrow NO_2F_{(g)}$ (fast)
Identify the reaction intermediate.

For the reaction between $A$ and $B$,the initial rate of reaction $(r_0)$ was measured for different initial concentrations of $A$ and $B$ as given below. Determine the order of the reaction with respect to $A$ and $B$ respectively.

$[A] / mol \ L^{-1}$	$0.2, 0.2, 0.4$
$[B] / mol \ L^{-1}$	$0.3, 0.1, 0.05$
$r_0 / mol \ L^{-1} s^{-1}$	$5.0 \times 10^{-5}, 5.0 \times 10^{-5}, 1.4 \times 10^{-4}$

The experimental data for the reaction $2A + B_2 \longrightarrow 2AB$ is given below:

Exp.	$[A] \ (mol \ L^{-1})$	$[B_2] \ (mol \ L^{-1})$	Rate $(mol \ L^{-1} \ S^{-1})$
$1$	$0.50$	$0.50$	$1.6 \times 10^{-4}$
$2$	$0.50$	$1.00$	$3.2 \times 10^{-4}$
$3$	$1.00$	$1.00$	$3.2 \times 10^{-4}$

Determine the rate law for the reaction.

Find the rate law for the reaction,$CHCl_{3(g)} + Cl_{2(g)} \rightarrow CCl_{4(g)} + HCl_{(g)}$ if the order of reaction with respect to $CHCl_{3(g)}$ is $1$ and with respect to $Cl_{2(g)}$ is $1/2$.

If the rate expression for a chemical reaction is given by $\text{Rate} = k[A]^m[B]^n$,what is the order of the reaction?