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>
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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