Use the right tool for the job. This here is nowhere near a full implementation of a ASCII renderer for MathML, but it's a start that will work for your one example document.

<?xml version="1.0" encoding="utf-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Tr
+ansform">
<xsl:output method="text" encoding="us-ascii"/>
<xsl:strip-space elements="*" />

<xsl:template match="@*|node()">
    <xsl:apply-templates select="@*|node()" />
</xsl:template>

<xsl:template match="ci|cn">
    <xsl:value-of select="." />
</xsl:template>

<xsl:template match="divide"> / </xsl:template>
<xsl:template match="power"> ^ </xsl:template>

<xsl:template match="apply">
    <xsl:variable name="operator">
        <xsl:apply-templates select="*[1]" />
    </xsl:variable>

    <xsl:text>(</xsl:text>

    <xsl:apply-templates select="*[2]" />
    <xsl:for-each select="*[position() > 2]">
        <xsl:copy-of select="$operator" />
        <xsl:apply-templates select="." />
    </xsl:for-each>

    <xsl:text>)</xsl:text>
</xsl:template>

</xsl:stylesheet>
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This translates your sample input to

(joule / (meter ^ 2))

Yes, XSLT is horribly verbose, but if you can see past the long-winded identifiers and the redundancy caused by closing tags, you'll find the basic modus operandi of the language to be a compact, elegant way of expressing tree manipulations. (I've often toyed with the idea of writing a strictly lexical translator that would allow transformations to be expressed in a less redundant, more human friendly syntax.)

The following could be used as a driver script if you need to do this from Perl.

#!/usr/bin/perl
use strict;
use warnings;

use XML::LibXSLT;
use XML::LibXML;

my $parser = XML::LibXML->new();

my $mathml = $parser->parse_string( do { local $/; <> } );

my $xform_src = $parser->parse_fh( \*DATA );

my $xform = XML::LibXSLT->new()->parse_stylesheet( $xform_src );

my $results = $xform->transform( $mathml );

print $xform->output_string( $results );

__END__
paste stylesheet here...
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Makeshifts last the longest.