document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012690>Question 1012690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me solve a^1/2 /a^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628684 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=628684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 2 laws of exponents that are operating here.\r<BR>\n" );
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document.write( "the first is that x^a/x^b = x^(a-b)\r<BR>\n" );
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document.write( "the second is that x^-a = 1/x^a\r<BR>\n" );
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document.write( "we'll apply them both to your problem.\r<BR>\n" );
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document.write( "start with a^(1/2) / a^2.\r<BR>\n" );
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document.write( "by the first law, this becomes a^(1/2-2) which becomes a^(-3/2).\r<BR>\n" );
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document.write( "by the second law, this becomes 1/a^(3/2).\r<BR>\n" );
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document.write( "if this is correct, we can pick any value of a and we'll get the desired result.\r<BR>\n" );
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document.write( "let's let a = 4.\r<BR>\n" );
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document.write( "then 1/a^(3/2) = 1/4^(3/2) = 1/8.\r<BR>\n" );
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document.write( "now we see if that's the same as when we do a^(1/2) / a^2.\r<BR>\n" );
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document.write( "a^(1/2) = 2<BR>\n" );
document.write( "a^2 = 4^2 = 16<BR>\n" );
document.write( "2/16 = 1/8<BR>\n" );
document.write( "same answer so we're good.\r<BR>\n" );
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