document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=495996>Question 495996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am confused by this question, particularly because of the variable being used instead of a real number.<BR>\n" );
document.write( "Rewrite without exponents:<BR>\n" );
document.write( "x^1/4 (fraction, not division)\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 #336289 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=336289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^(1/4) is the expression.\r<BR>\n" );
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document.write( "you are taking x and raising it to the power of (1/4)\r<BR>\n" );
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document.write( "raising something to the power of (1/n) means taking the nth root of that something.\r<BR>\n" );
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document.write( "in this expression, you are taking the 4th root of x.\r<BR>\n" );
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document.write( "that would be shown as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in general, the expression of:\r<BR>\n" );
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document.write( "x^(a/b) raises x to the power of a and then takes the bth root of the result.<BR>\n" );
document.write( "alternatively, x^(a/b) takes the bth root of x and then raises it to the power of a.\r<BR>\n" );
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document.write( "an example will help clarify this:\r<BR>\n" );
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document.write( "x^(5/4) is the same as (x^5)^(1/4) which is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%5E5%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x^(5/4) is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%284%2Cx%29%29%5E5 ALIGN=MIDDLE  ALT=\"%28root%284%2Cx%29%29%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "an example will help clarify this.\r<BR>\n" );
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document.write( "let x = 16<BR>\n" );
document.write( "x^5 = 16^5 = 1048576<BR>\n" );
document.write( "1048576^(1/4) = 32\r<BR>\n" );
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document.write( "same example, only working the other way (taking the root first and then taking the power).\r<BR>\n" );
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document.write( "let x = 16<BR>\n" );
document.write( "x^(1/4) = 2<BR>\n" );
document.write( "2^5 = 32\r<BR>\n" );
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document.write( "whether you take the root first or you raise to the power first doesn't matter.<BR>\n" );
document.write( "you get the same answer each time.\r<BR>\n" );
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document.write( "your problem is:\r<BR>\n" );
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document.write( "x^(1/4)<BR>\n" );
document.write( "they want you to rewrite without exponents.<BR>\n" );
document.write( "x^(1/4) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "an example:\r<BR>\n" );
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document.write( "let x = 16<BR>\n" );
document.write( "x^(1/4) becomes:<BR>\n" );
document.write( "16^(1/4) which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C16%29 ALIGN=MIDDLE  ALT=\"root%284%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals 2\r<BR>\n" );
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document.write( "the rules are:\r<BR>\n" );
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document.write( "x<sup>(a/b)</sup> = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%28b%2Cx%29%29%5Ea ALIGN=MIDDLE  ALT=\"%28root%28b%2Cx%29%29%5Ea\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28b%2Cx%5Ea%29 ALIGN=MIDDLE  ALT=\"root%28b%2Cx%5Ea%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in your problem, a was equal to 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E1 ALIGN=MIDDLE  ALT=\"x%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is just shown as x.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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