document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20301>Question 20301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried every way i can think of to simplify this type of equation and have looked through my book, please help me find out how to do these problems. I would really appreciate it if someone could help me with this problem.<BR>\n" );
document.write( "One of the questions is:\r<BR>\n" );
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document.write( "In this and the following problem, simplify the expression and enter the resulting exponent as a fraction, after canceling common factors in numerator and denominator. \r<BR>\n" );
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document.write( "(x^2/3 x^1/4)/x^1/7=x^r       <BR>\n" );
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document.write( "where r=?/? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9797 by </B><A HREF=/tutors/aboutme.mpl?userid=suresh><B>suresh(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=suresh><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=9797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "(x^2/3 x^1/4)/(x^1/7)=x^r.\r<BR>\n" );
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document.write( "Law of indices:<BR>\n" );
document.write( " x^m * x^n = x^(m+n)-------(1)\r<BR>\n" );
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document.write( " x^x / x^n = x^(m-n) ------(2)\r<BR>\n" );
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document.write( "Law of exponents:<BR>\n" );
document.write( "x^m = x^n if and only if m = n -----(3)\r<BR>\n" );
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document.write( "x^r = x^(2/3 + 1/4 )/x^1/7  (Using (1))\r<BR>\n" );
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document.write( "    = x^(11/12)/x^1/7       (Simplifying by LCD Method)\r<BR>\n" );
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document.write( "    = x^(11/12 - 1/7 )       (Using (2))\r<BR>\n" );
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document.write( "    = x^(65/84)\r<BR>\n" );
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document.write( "Therefore, x^r = x^65/84\r<BR>\n" );
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document.write( "---->  r = 65 / 84  (Using 3)\r<BR>\n" );
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document.write( "Hence r = 65 /84<BR>\n" );
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