document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95098>Question 95098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't understand how to simplify this question:\r<BR>\n" );
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document.write( "(16 raised to the negative 1 power, \"x\" raised to the negative 4th power, \"y\" raised to the possitive 12th power) This whole problem is in parenthesis. Outside of the parenthesis, the entire problem is raisd to negative 3/4.\r<BR>\n" );
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document.write( "I hope this makes sense.\r<BR>\n" );
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document.write( "So I think it should be written as:\r<BR>\n" );
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document.write( "(16^-1 x^-4 y^12)^-3/4 \r<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 #69300 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=69300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2816%5E%28-1%29%29%28+x%5E%28-4%29+%29%28y%5E12%29%29%5E%28-3%2F4%29+ ALIGN=MIDDLE  ALT=\"%28%2816%5E%28-1%29%29%28+x%5E%28-4%29+%29%28y%5E12%29%29%5E%28-3%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By the power rule of exponents you multiply each of the exponents inside the parentheses<BR>\n" );
document.write( "by the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "When you do that the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2816%5E%28%28-1%29%2A%28-3%2F4%29%29%29%2A%28+x%5E%28%28-4%29%2A%28-3%2F4%29%29+%29%2A%28y%5E%28%2812%29%2A%28-3%2F4%29%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note ... for some reason the 3 in the numerator of each multiplication gets clipped off.<BR>\n" );
document.write( "Hope this doesn't confuse you.<BR>\n" );
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document.write( "Do the multiplication by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in each of the exponents and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2816%5E%283%2F4%29%29%2A%28+x%5E%283%29%29%2A%28y%5E%28-9%29%29%29 ALIGN=MIDDLE  ALT=\"%28%2816%5E%283%2F4%29%29%2A%28+x%5E%283%29%29%2A%28y%5E%28-9%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "At this point, let's just focus on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"16%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can work the power rule in reverse and<BR>\n" );
document.write( "get two different forms of this as follows:<BR>\n" );
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document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%5E%281%2F4%29%29%5E3 ALIGN=MIDDLE  ALT=\"%2816%5E%281%2F4%29%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%5E3%29%5E%281%2F4%29%29 ALIGN=MIDDLE  ALT=\"%2816%5E3%29%5E%281%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Applying the power rule to either of these gets you back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"16%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So to evaluate this term we can either find the fourth root of 16 and cube it, or we can<BR>\n" );
document.write( "cube 16 and take the fourth root of that answer.  In this case it's easier to find the <BR>\n" );
document.write( "fourth root of 16 which is 2 and cube that to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3+=+8 ALIGN=MIDDLE  ALT=\"2%5E3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the answer. So now we<BR>\n" );
document.write( "can replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"16%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the problem is then down to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3y%5E%28-9%29 ALIGN=MIDDLE  ALT=\"8x%5E3y%5E%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But if a term in the numerator has a minus exponent, you can put that same term in the <BR>\n" );
document.write( "denominator with a positive exponent. So we can change <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E%28-9%29 ALIGN=MIDDLE  ALT=\"y%5E%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by putting it in the<BR>\n" );
document.write( "denominator as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E9 ALIGN=MIDDLE  ALT=\"y%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the answer to this problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2Fy%5E9 ALIGN=MIDDLE  ALT=\"8x%5E3%2Fy%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that in taking the fourth root of x and y, to get real answers we must limit<BR>\n" );
document.write( "both of these variables to positive values. Therefore, we need to make the answer have<BR>\n" );
document.write( "positive values of x and y which we can do through absolute values.  Therefore, the answer is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A%28abs%28x%29%29%5E3%2F%28abs%28y%29%29%5E9 ALIGN=MIDDLE  ALT=\"8%2A%28abs%28x%29%29%5E3%2F%28abs%28y%29%29%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem. </SPAN>\n" );
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