# Use only exponents (no radicals) in output expressions

Radical symbols ($\sqrt{\,\,\,\,}$) are the devil. Is there any way to get mathematica to never use them, and instead express everything as an exponential?

i.e. I want

In[1]:= Sqrt[x]


to give $x^{1/2}$ instead of $\sqrt{x}$.

• Does $Post=(#/.Power[x_,Rational[a_,b_]]:>HoldForm[x]^HoldForm[(a/b)])& do what you want? – ciao Jun 1, 2014 at 1:49 • @rasher You should be using Defer rather than HoldForm so that output can be used as input. Also I don't think holding x is necessary. Jun 1, 2014 at 6:40 • @Mr.Wizard: Yeah, just threw out an idea - this kind of thing is something I've never had any real need to do. – ciao Jun 1, 2014 at 6:56 ## 2 Answers I think I would choose to use MakeBoxes and Defer for this: MakeBoxes[a_^Rational[1, x_], fmt_] := ToBoxes[a^Defer[1/x], fmt]  Now: -Sqrt[a - bar]  -(a - bar)^(1/2)  This also catches cases that use RadicalBox: x^(1/3) // TraditionalForm  x1/3 Defer is used to allow the output to be used as input. An alternative is Interpretation but that seems like overkill here. Instead of MakeBoxes definition you could use $PrePrint, assuming it is not already in use or you will append a rule to an existing definition. It is clean but gives you less control over specific formatting.

$PrePrint = # /. a_^Rational[1, x_] :> a^Defer[1/x] &;  If these miss some cases or change things that should not be changed (undetermined), you could instead intercept all box conversions and replace SqrtBox and RadicalBox: lhs : MakeBoxes[arg__] /; ! TrueQ[$sqrtReplace] :=
Block[{$sqrtReplace = True}, lhs /. { SqrtBox[a_] :> SuperscriptBox[a, RowBox[{"1", "/", "2"}]], RadicalBox[a_, x_] :> SuperscriptBox[a, RowBox[{"1", "/", x}]] } ]  This should be avoided if possible as it is a costly operation. (It will add overhead to all output generation.) • This looks great in a new notebook! How can I append this rule to my previous$PrePrint (i.e. the previous thread)? Jun 1, 2014 at 14:34
• @zhermes I suggested MakeBoxes so that that would not be necessary, but if you wish you could use: $PrePrint = If[$note =!= Null, # &[Row[{Pane@#, Spacer[50], $note}],$note = Null], #] &[ ScientificForm@PowerExpand@# /. a_^Rational[1, x_] :> a^Defer[1/x]] &;. Incidentally I made a mistake in the prior answer which I will now correct. Jun 2, 2014 at 3:39
• Also, it looks like this (the solution from your comment, not using the 'interception') doesn't work for radicals in the denominator. Is this an issue with catching a '-1/2' instead of '+1/2' ? Jun 2, 2014 at 14:56
• @zhermes You're right, I'd need to allow for Rational[-1,2] there. That also raises the question of which format you prefer: foo/-Sqrt[a - bar] could render as either -(foo/(a - bar)^(1/2)) or -(a - bar)^(-(1/2)) foo. Jun 2, 2014 at 20:57

If you look at the FullForm, you will see that it already uses the exponential form:

Sqrt[x] // FullForm
(* -> Power[x, Rational[1, 2]] *)

x^(1/2) // FullForm
(* -> Power[x, Rational[1, 2]] *)

Sqrt[x] === x^(1/2)
(* -> True *)

• I would argue that it doesn't use exponential form, it uses verbose-descriptions-form :) Jun 1, 2014 at 14:24