document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107733>Question 107733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expressions by using the properties of rational exponents.  Write the final answer using positive exponents only.\r<BR>\n" );
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document.write( "(50p^-1q)^1/2 (this is the numerator)<BR>\n" );
document.write( "(2pq^-3)^1/2 (this is the denominator)\r<BR>\n" );
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document.write( "I don't have a clue.  Please help.<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 #78503 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78503\">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=%28%2850p%5E%28-1%29q%29%5E%281%2F2%29%29%2F%282pq%5E%28-3%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%2850p%5E%28-1%29q%29%5E%281%2F2%29%29%2F%282pq%5E%28-3%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Yes, indeed that is ugly.  But fortunately, the exponent on the numerator and denominator is the same, so we can take this first step:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2850p%5E%28-1%29q%29%2F%282pq%5E%28-3%29%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%2850p%5E%28-1%29q%29%2F%282pq%5E%28-3%29%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, any coefficient with a negative exponent can move from the numerator to the denominator, or vice versa, making the exponent positive.  That's because of the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28-n%29=1%2F%28a%5En%29 ALIGN=MIDDLE  ALT=\"a%5E%28-n%29=1%2F%28a%5En%29\"   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%2850q%5E4%29%2F%282p%5E2%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%2850q%5E4%29%2F%282p%5E2%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And then divide the 50 by the 2 in the denominator to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2825q%5E4%29%2F%28p%5E2%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%2825q%5E4%29%2F%28p%5E2%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F2%29=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F2%29=sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Applying this rule we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2825q%5E4%29%2Fp%5E2%29=%28sqrt%2825q%5E4%29%29%2F%28sqrt%28p%5E2%29%29=%285q%5E2%29%2Fp ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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