After traversing your continuous path, you finally arrive at Gate $5.$ Your computer reads the gate's directions to you.$$The passcode for this gate is the number found by first entering m$(1)$and then entering n$(4)$using the definitions below.$$ What values do you provide to your computer?

f$($x$)=($x$^62$x$)$

g$($x$)=($x$2+6$x$39)$

h$($x$)=2$x$7$

m$($x$)=$f$($x$)$g$($x$)$

n$($x$)=$g$($x$)/$h$($x$)$