document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152334>Question 152334</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495389730/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I can't seem to figure this problem out. Need some serious help!<BR>\n" );
document.write( "I am suppose to simplify the radical square root 54xy^7 over square root 6xy. Assume that all variables represent positive numbers.<BR>\n" );
document.write( "I appreciate anybody that can help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111986 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=111986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2854xy%5E7%29%2Fsqrt%286xy%29 ALIGN=MIDDLE  ALT=\"sqrt%2854xy%5E7%29%2Fsqrt%286xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2854xy%5E7%29%2F%286xy%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2854xy%5E7%29%2F%286xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289y%5E6%29 ALIGN=MIDDLE  ALT=\"sqrt%289y%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2854xy%5E7%29%2F%286xy%29 ALIGN=MIDDLE  ALT=\"%2854xy%5E7%29%2F%286xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2854xy%5E7%29%2F%286xy%29=%2854%2F6%29%28%28xy%5E7%29%2F%286xy%29%29=9x%5E%281-1%29y%5E%287-1%29=9x%5E0y%5E6=9y%5E6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(9y^6\right)^{\frac{1}{2}}\"> Convert from radical notation to exponent notation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\left(9\right)^1y^6\right)^{\frac{1}{2}}\"> Rewrite <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 9\"> as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(9\right)^1\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(9\right)^{\left(1\right)\left(\frac{1}{2}\right)}y^{\left(6\right)\left(\frac{1}{2}\right)}\"> Multiply the outer exponent by each of the inner exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(9\right)^{\frac{1}{2}}y^{3}\"> Multiply the exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29y%5E3 ALIGN=MIDDLE  ALT=\"sqrt%289%29y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert back to radical notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E3 ALIGN=MIDDLE  ALT=\"3y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 9 to get 3\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2854xy%5E7%29%2Fsqrt%286xy%29 ALIGN=MIDDLE  ALT=\"sqrt%2854xy%5E7%29%2Fsqrt%286xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E3 ALIGN=MIDDLE  ALT=\"3y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2854xy%5E7%29%2Fsqrt%286xy%29=3y%5E3 ALIGN=MIDDLE  ALT=\"sqrt%2854xy%5E7%29%2Fsqrt%286xy%29=3y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E0 ALIGN=MIDDLE  ALT=\"y%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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