document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463027>Question 463027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I find the radical expression of 4 over a^9<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317337 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=317337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4/a^9 = 4*a^(-9)\r<BR>\n" );
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document.write( "this is because of the law of exponents that states that a^(-b) = 1/a^b.\r<BR>\n" );
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document.write( "4 * a^(-9) = 4 * 1/a^9 = 4/a^9.\r<BR>\n" );
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document.write( "not sure if this is what you want, but that's the equivalent expression.\r<BR>\n" );
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document.write( "if you are asking how to solve for a, you would do the following:\r<BR>\n" );
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document.write( "set the expression equal to some value which we'll call y.\r<BR>\n" );
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document.write( "you will get the equation y = 4/a^9\r<BR>\n" );
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document.write( "multiply both sides of this equation by a^9 and divide both sides of this equation by y to get a^9 = (4/y)\r<BR>\n" );
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document.write( "take the 9th root of both sides of this equation to get a = (4/y)^(1/9) which is equivalent to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+root%289%2C%284%2Fy%29%29 ALIGN=MIDDLE  ALT=\"y+=+root%289%2C%284%2Fy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when you know the value of y, you can solve for a.\r<BR>\n" );
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document.write( "an example:\r<BR>\n" );
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document.write( "your expression is 4/a^9.\r<BR>\n" );
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document.write( "let y = 3000.\r<BR>\n" );
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document.write( "your equation is y = 4/a^9 which becomes 3000 = 4/a^9.\r<BR>\n" );
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document.write( "you solve for a to get a = (4/3000)^(1/9) which becomes a = .479235243\r<BR>\n" );
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document.write( "you confirm this by plugging that value for a in the original equation of 3000 = 4/a^9 which gets you  3000 = 4/(.479235243^9) = 4/.0013333333 = 3000, confirming the answer is good.\r<BR>\n" );
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