document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557665>Question 557665</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Im having problems wit this particular expression. Could someone help me out please<BR>\n" );
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document.write( "(16x^8y^12)1/2<BR>\n" );
document.write( "(161/2)(x^8)1/2(y^12)1/2<BR>\n" );
document.write( "(16)^-1 x^4 y^6<BR>\n" );
document.write( "1/16 1/x^4 1/y^6<BR>\n" );
document.write( "y^6/16x^4<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 #362714 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5397)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your question is confusing, so I assume you are confused. As a result I may end up answering the wrong question, or confusing you even worse.<BR>\n" );
document.write( "Maybe your expression was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E8y%5E12%29%281%2F2%29 ALIGN=MIDDLE  ALT=\"%2816x%5E8y%5E12%29%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If so the answer is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E8y%5E12%29%281%2F2%29 ALIGN=MIDDLE  ALT=\"%2816x%5E8y%5E12%29%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2A%281%2F2%29%29x%5E8y%5E12 ALIGN=MIDDLE  ALT=\"%2816%2A%281%2F2%29%29x%5E8y%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E8y%5E12 ALIGN=MIDDLE  ALT=\"8x%5E8y%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There was not much anyone could do with that expression.<BR>\n" );
document.write( "There are a few \"grammar\" rules for reading and writing algebra. They are very few. The rest are logical conclusions, like the need to take off your shoes before taking off your socks. They are obvious if you are not in panic mode. Unfortunately math and algebra cause a lot of unnecessary panic.<BR>\n" );
document.write( "The \"grammar\" rules for writing algebra say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E8y%5E12 ALIGN=MIDDLE  ALT=\"16x%5E8y%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E12 ALIGN=MIDDLE  ALT=\"y%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be calculated first, if you could do it.<BR>\n" );
document.write( "However, there's nothing you can do with them, so they will carry unchanged to the end, like so much undigestible fiber.<BR>\n" );
document.write( "You have three factors inside the parenthesis: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E12 ALIGN=MIDDLE  ALT=\"y%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A fourth factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is outside the parenthesis.<BR>\n" );
document.write( "All four factors are multiplied together. Although multiplication is done two factors at a time, when all you are doing is multiplications, the order and the grouping do not matter. So when they write the calculation for the volume of a box as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A9%2A2 ALIGN=MIDDLE  ALT=\"5%2A9%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > it really means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A9%29%2A2 ALIGN=MIDDLE  ALT=\"%285%2A9%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but no one bother to write the parentheses.<BR>\n" );
document.write( "The result can also be calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%289%2A2%29 ALIGN=MIDDLE  ALT=\"5%2A%289%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A2%29%2A9 ALIGN=MIDDLE  ALT=\"%285%2A2%29%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You will use all your factors, but can choose how to do it. You grab any two factors, multiply them together, and then multiply the result times the other factor. You would not care which two dimensions of a box you multiply together first. The volume of the box is the same, anyway you calculate it.<BR>\n" );
document.write( "In the case of your problem, the only two factors you can do anything with are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so after you multiply those two together, you are done. You leave the rest of the multiplications indicated.\r<BR>\n" );
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