document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825459>Question 825459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Am solving a 7th grade text book and came across this question.\r<BR>\n" );
document.write( "\n" );
document.write( "81^x = 1/(125^y) where x and y are integers. Find 12xy.\r<BR>\n" );
document.write( "\n" );
document.write( "The answer given is 0. While I can understand that when x & y are 0 the above equation is satisfied, I can't seem to figure how to arrive at the conclusion.\r<BR>\n" );
document.write( "\n" );
document.write( "I tried something like:\r<BR>\n" );
document.write( "\n" );
document.write( "--> (3^4x)(5^3y) = 1 --> 3^(4x + 3ky) = 1 where k is such that 3^k = 5 --> 4x + 3ky = 0\r<BR>\n" );
document.write( "\n" );
document.write( "But with the above am not able to establish that 12xy is 0.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497326 by </B><A HREF=/tutors/aboutme.mpl?userid=unlockmath><B>unlockmath(1688)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=unlockmath><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=unlockmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello, <BR>\n" );
document.write( "Let's try it this way, it might make more sense. Set it up as a proportion:<BR>\n" );
document.write( "81^x/1 = 1/(125^y)<BR>\n" );
document.write( "Now cross multiply. <BR>\n" );
document.write( "1=(81^x)(125^y)<BR>\n" );
document.write( "From this we can see the only numbers that satisfy the equation is 0 for x and y.<BR>\n" );
document.write( "Does that help?<BR>\n" );
document.write( "RJ<BR>\n" );
document.write( "www.math-unlock.com </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );