prefix: +xy
  infix: x+y
postfix: xy+

 prefix: -*abc
  infix: a*b-c
postfix: ab*c-

 prefix: /-^b2**4ac*2a
  infix: (b^2-4*a*c)/(2*a)
postfix: b2^4a*c*-2a*/

 prefix: **+ag+bc*++cd+de++efg
  infix: (a+g)*(b+c)*(c+d+d+e)*(e+f+g)
postfix: ag+bc+*cd+de++ef+g+**

 prefix: /^2+a*bc-e-fg
  infix: 2^(a+b*c)/(e-(f-g))
postfix: 2abc*+^efg--/

 prefix: /^2*a^bc--ehg
  infix: 2^(a*b^c)/(e-h-g)
postfix: 2abc^*^eh-g-/

 prefix: /^2*a^bc//xy/hg
  infix: 2^(a*b^c)/(x/y/(h/g))
postfix: 2abc^*^xy/hg///