document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277573>Question 277573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having some difficulties working functions which have numbers raised to fractional powers, like the following question.\r<BR>\n" );
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document.write( "Solve: x^(2/3) - 2x^(1/3) - 15 = 0\r<BR>\n" );
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document.write( "I understand using a placeholder thing, reorganizing the problem, and then solving for the placeholder, but I am having problems with raising to the fractional powers while solving for X. Could you explain how please?\r<BR>\n" );
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document.write( "I got this question solved down to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+u%5E2+-+2u+-15+=+0+ ALIGN=MIDDLE  ALT=\"+u%5E2+-+2u+-15+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where u = x^(1/3) The possible solutions for u are 5, and -3. I need help solving for X now.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202086 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=202086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E%281%2F3%29%5E%22%22 ALIGN=MIDDLE  ALT=\"u=x%5E%281%2F3%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can convert to radical notation to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"u=root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It's just a different way to same thing.\r<BR>\n" );
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document.write( "Now because the possible solutions for 'u' (no pun intended) are 5 and -3, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5 ALIGN=MIDDLE  ALT=\"u=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-3 ALIGN=MIDDLE  ALT=\"u=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's find the solution(s) in terms of 'x' when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5 ALIGN=MIDDLE  ALT=\"u=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"u=root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"5=root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5 ALIGN=MIDDLE  ALT=\"u=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%5E3=%28root%283%2Cx%29%29%5E3 ALIGN=MIDDLE  ALT=\"%285%29%5E3=%28root%283%2Cx%29%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube both sides to undo the cube root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%5E3=x ALIGN=MIDDLE  ALT=\"%285%29%5E3=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube the cube root of 'x' to just get 'x'.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125=x ALIGN=MIDDLE  ALT=\"125=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube 5 to get 125.\r<BR>\n" );
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document.write( "So one solution in terms of 'x' is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=125 ALIGN=MIDDLE  ALT=\"x=125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's find the solution(s) in terms of 'x' when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-3 ALIGN=MIDDLE  ALT=\"u=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"u=root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"-3=root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-3 ALIGN=MIDDLE  ALT=\"u=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E3=%28root%283%2Cx%29%29%5E3 ALIGN=MIDDLE  ALT=\"%28-3%29%5E3=%28root%283%2Cx%29%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube both sides to undo the cube root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E3=x ALIGN=MIDDLE  ALT=\"%28-3%29%5E3=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube the cube root of 'x' to just get 'x'.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27=x ALIGN=MIDDLE  ALT=\"-27=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube -3 to get -27.\r<BR>\n" );
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document.write( "So another solution in terms of 'x' is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-27 ALIGN=MIDDLE  ALT=\"x=-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the solutions in terms of 'x' are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=125 ALIGN=MIDDLE  ALT=\"x=125\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-27 ALIGN=MIDDLE  ALT=\"x=-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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