document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135939>Question 1135939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 216^-2k<BR>\n" );
document.write( "-------- = 36   Please show steps and solution.<BR>\n" );
document.write( "36^-2k-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753695 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=753695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216%5E%28-2k%29%2F36%5E%28-2k-3%29+=+36 ALIGN=MIDDLE  ALT=\"216%5E%28-2k%29%2F36%5E%28-2k-3%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There are of course many paths to solving this equation....<br><BR>\n" );
document.write( "With the negative exponents in both numerator and denominator, I would first switch them to make the exponents positive:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%5E%282k%2B3%29%2F216%5E%282k%29+=+36 ALIGN=MIDDLE  ALT=\"36%5E%282k%2B3%29%2F216%5E%282k%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then, with bases 36=6^2 and 216=6^3 as the bases for the exponents, change every term in the equation to have base 6:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%5E2%29%5E%282k%2B3%29%2F%286%5E3%29%5E%282k%29+=+6%5E2 ALIGN=MIDDLE  ALT=\"%286%5E2%29%5E%282k%2B3%29%2F%286%5E3%29%5E%282k%29+=+6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E%284k%2B6%29%2F6%5E%286k%29+=+6%5E2 ALIGN=MIDDLE  ALT=\"6%5E%284k%2B6%29%2F6%5E%286k%29+=+6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E%28-2k%2B6%29+=+6%5E2 ALIGN=MIDDLE  ALT=\"6%5E%28-2k%2B6%29+=+6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The bases are the same, so the exponents are equal:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2k%2B6+=+2 ALIGN=MIDDLE  ALT=\"-2k%2B6+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2k+=+-4 ALIGN=MIDDLE  ALT=\"-2k+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+2 ALIGN=MIDDLE  ALT=\"k+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );