V$.(20$ points$)$ In a computer network, the IP address of one of the hosts is $156\mathrm{.}43\mathrm{.}167\mathrm{.}1/22.$

$(1)$ Find the network ID $($in a$.$b$.$c$.$d$/$x form$).$

$(2)$ Find the broadcast address of the network.

$(3)$ What is the maximum number of IP addresses that can be assigned to hosts in this network?

$(4)$ Suppose we need to create four subnets in this network. Subnet $1$ has $208$ hosts, subnet $2$ has $410$ hosts, subnet $3$ has $90$ hosts and subnet $4$ has $40$ hosts. What are the prefixes $($ of form a$.$b$.$c$.$d$/$x$)$ for the four subnets? Show all steps to justify your answer. $($Answers without correct justification may receive no credit.$)$