document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154445>Question 154445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is the set of irrational numbers closed under exponentation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113718 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=113718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No it is not. Here is a counterexample: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%29%5E2=3 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%29%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since 3 is rational, this shows that the set of irrational numbers is <b>not</b> closed under exponentiation. </SPAN>\n" );
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