document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=716905>Question 716905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify.\r<BR>\n" );
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document.write( "((x^-2) / (2y^-1)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440069 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=440069\">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=x%5E%28-2%29+%2F+%282%28y%5E%28-1%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29+%2F+%282%28y%5E%28-1%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Of course must follow the order of operations (aka PEMDAS or GEMDAS). So we start with the power of a power in the denominator. The rule here is to multiply the exponents:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29+%2F+%282y%5E%28-2%29%29 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29+%2F+%282y%5E%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a simplified expression... unless you consider negative exponents \"unsimplified\". If this is so then we can eliminate the negative exponents quickly or slowly.<br><BR>\n" );
document.write( "Quickly.<BR>\n" );
document.write( "The fast way is to understand that negative exponents mean reciprocals. A negative exponent on a factor in the numerator becomes that factor with a positive exponent in the denominator and vice versa. Using this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29+%2F+%282y%5E%28-2%29%29 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29+%2F+%282y%5E%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2F+%282x%5E2%29 ALIGN=MIDDLE  ALT=\"y%5E2+%2F+%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the simplified expression with positive exponents. (Note: Exponents only apply to whatever is immediately in front of it! So the exponent of -2 in the denominator applies only to the y, not to the 2! This is why the 2 stays in the denominator.)<br><BR>\n" );
document.write( "Slowly.<BR>\n" );
document.write( "The methodical way is to use the rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28-n%29+=+1%2Fa%5En ALIGN=MIDDLE  ALT=\"a%5E%28-n%29+=+1%2Fa%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using this rule on the two negative exponents in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29+%2F+%282y%5E%28-2%29%29 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29+%2F+%282y%5E%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%5E2%29%2F%282%281%2Fy%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2Fx%5E2%29%2F%282%281%2Fy%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%5E2%29%2F%282%2Fy%5E2%29%29 ALIGN=MIDDLE  ALT=\"%281%2Fx%5E2%29%2F%282%2Fy%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying the numerator and denominator of the \"big\" fraction by the lowest common denominator of the \"little\" fractions, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, will eliminate the \"little\" fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Fx%5E2%29%2F%282%2Fy%5E2%29%29%2A%28%28x%5E2y%5E2%29%2F%28x%5E2y%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2Fx%5E2%29%2F%282%2Fy%5E2%29%29%2A%28%28x%5E2y%5E2%29%2F%28x%5E2y%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "giving us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2F+%282x%5E2%29 ALIGN=MIDDLE  ALT=\"y%5E2+%2F+%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );