document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202091>Question 202091</A>: <I><SPAN STYLE=\"word-break: break-all;\">  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152358 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=152358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify these following expressions:<BR>\n" );
document.write( "(2x)^4 x^3<BR>\n" );
document.write( "(-3y)^4<BR>\n" );
document.write( "(3z)^2(6z^2)^-3<BR>\n" );
document.write( "5x2&#8260;25x5<BR>\n" );
document.write( "10(x+y)^4/5(x+y)^3<BR>\n" );
document.write( "1/6x(3x^2)^3<BR>\n" );
document.write( "(5x^2)^3(1/25x^4)^2<BR>\n" );
document.write( "(2z^2)^-5*z^-10<BR>\n" );
document.write( "(3/x)^4(4/x)^-2<BR>\n" );
document.write( "[2(r-s)]^2/(r-s)^3\r<BR>\n" );
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document.write( "Let's take a few at a time......\r<BR>\n" );
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document.write( "I see your first problem as this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E4 ALIGN=MIDDLE  ALT=\"%282x%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3 ALIGN=MIDDLE  ALT=\"+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If that is the problem, then you multiply:\r<BR>\n" );
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document.write( "2 to the 4th power -- 2*2*2*2 = 16  (You distribute the exponent \"4\" to the 2 and to the \"x\"....\r<BR>\n" );
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document.write( "and then you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4 ALIGN=MIDDLE  ALT=\"x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the bases are the same, you ADD the exponents, so you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E7 ALIGN=MIDDLE  ALT=\"x%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FINAL answer:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E7 ALIGN=MIDDLE  ALT=\"16x%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next:(-3y)^4\r<BR>\n" );
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document.write( "That is:  -3*-3*-3*-3 = 81  (See how the exponent 4 is distributed to the -3 and to the y?)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4 ALIGN=MIDDLE  ALT=\"y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the second part of the answer\r<BR>\n" );
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document.write( "FINAL answer:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81y%5E4 ALIGN=MIDDLE  ALT=\"81y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next:  (3z)^2(6z^2)^-3\r<BR>\n" );
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document.write( "If the problem is this:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283z%29%5E2 ALIGN=MIDDLE  ALT=\"%283z%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6z%5E2 ALIGN=MIDDLE  ALT=\"6z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > raised to the power of -3<BR>\n" );
document.write( "That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z%5E2 ALIGN=MIDDLE  ALT=\"9z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E-3 ALIGN=MIDDLE  ALT=\"6%5E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E-6 ALIGN=MIDDLE  ALT=\"z%5E-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That becomes:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z%5E2 ALIGN=MIDDLE  ALT=\"9z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > *  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6%5E3z%5E6 ALIGN=MIDDLE  ALT=\"1%2F6%5E3z%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Why?  The exponent \"2\" distributes to the 3 and to the z.\r<BR>\n" );
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document.write( "The exponent -3 distributes to the 6 and to the \"z\".  HOWEVER, for the \"z\", because you are raising a power to a power, you have to MULTIPLY the exponents. Therefore, the \"z\" becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E-6 ALIGN=MIDDLE  ALT=\"z%5E-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or.... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fz%5E6 ALIGN=MIDDLE  ALT=\"1%2Fz%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The problem is now:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z%5E2 ALIGN=MIDDLE  ALT=\"9z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216z%5E6 ALIGN=MIDDLE  ALT=\"216z%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "THAT becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F24+z%5E4 ALIGN=MIDDLE  ALT=\"1%2F24+z%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (we reduced the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F216 ALIGN=MIDDLE  ALT=\"9%2F216\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F24 ALIGN=MIDDLE  ALT=\"1%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let's stop here for a second and go over some exponent rules, k?   Then if you need help with your other answers, ask again.  It seems like you may not understand exponents...........\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >* <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5 ALIGN=MIDDLE  ALT=\"x%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  When multiplying... if the bases are the same, ADD the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >   When dividing... if the bases are the same, SUBTRACT the exponents\r<BR>\n" );
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document.write( "If you raise a power to a power, then MULTIPLY the exponents.  \r<BR>\n" );
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document.write( "If you have a NEGATIVE exponent in the NUMERATOR, just put it in the denominator and make it a POSITIVE exponent:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E-3 ALIGN=MIDDLE  ALT=\"x%5E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is really:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E3 ALIGN=MIDDLE  ALT=\"1%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you have a NEGATIVE EXPONENT in the DENOMINATOR, just put it in the numerator and make it a POSITIVE exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E-3 ALIGN=MIDDLE  ALT=\"1%2Fx%5E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is really:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope this helps......\r<BR>\n" );
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