document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174244>Question 174244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help! I've been show the rules, but I don't know how to apply them, could you please show me how? \r<BR>\n" );
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document.write( "3. Simplify the following expressions:\r<BR>\n" );
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document.write( "    a. X4 * X5 (4 & 5 are exponents, I don't know how to type that)\r<BR>\n" );
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document.write( "     b. Z9/Z10 (9 & 10 are exponents, I don't know how to type that)\r<BR>\n" );
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document.write( "    c. log3Y + log3Z (base 3)\r<BR>\n" );
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document.write( "    d. log5Y - log5Z (base 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129179 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Think of the problem as if there were no exponents involved<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+=+x%2Ax%2Ax%2Ax ALIGN=MIDDLE  ALT=\"x%5E4+=+x%2Ax%2Ax%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5+=+x%2Ax%2Ax%2Ax%2Ax ALIGN=MIDDLE  ALT=\"x%5E5+=+x%2Ax%2Ax%2Ax%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2Ax%5E5+=+x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax ALIGN=MIDDLE  ALT=\"x%5E4%2Ax%5E5+=+x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplied by itself <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > times, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2Ax%5E5+=+x%5E9 ALIGN=MIDDLE  ALT=\"x%5E4%2Ax%5E5+=+x%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Aha! You just add the exponents<BR>\n" );
document.write( "You can do any problem this way & discover the rule<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E9+=+z%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az ALIGN=MIDDLE  ALT=\"z%5E9+=+z%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E10+=+z%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az ALIGN=MIDDLE  ALT=\"z%5E10+=+z%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E9%2Fz%5E10+=+z%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az+%2F+%28z%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There's 1 more <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator, I'm left with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E9%2Fz%5E10+=+1%2Fz ALIGN=MIDDLE  ALT=\"z%5E9%2Fz%5E10+=+1%2Fz\"   DISABLED_style= \"max-width:90%; height:auto;\" > and I know<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fz+=+z%5E-1 ALIGN=MIDDLE  ALT=\"1%2Fz+=+z%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Aha!, I just do <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+-+10+=+-1 ALIGN=MIDDLE  ALT=\"9+-+10+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "As for logs, just do a very simple experiment<BR>\n" );
document.write( "How about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C16%29+%2B+log%282%2C64%29 ALIGN=MIDDLE  ALT=\"log%282%2C16%29+%2B+log%282%2C64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Big fact: ***** Logs are exponents!!! *****<BR>\n" );
document.write( "So I'm adding 2 exponents here<BR>\n" );
document.write( "The 1st term says: The exponent to the base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 2nd term says: The exponent to the base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the 1st case it's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4+=+16 ALIGN=MIDDLE  ALT=\"2%5E4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the 2nd case it's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E6+=+64 ALIGN=MIDDLE  ALT=\"2%5E6+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, now I,ve got<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C16%29+%2B+log%282%2C64%29+=+10 ALIGN=MIDDLE  ALT=\"log%282%2C16%29+%2B+log%282%2C64%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the sum of 2 logs, so it's a log.<BR>\n" );
document.write( "Express it as log(2,?) or \"log to the base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that gives me what?<BR>\n" );
document.write( "If I raise <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10+=+1024 ALIGN=MIDDLE  ALT=\"2%5E10+=+1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C16%29+%2B+log%282%2C64%29+=+log%282%2C1024%29 ALIGN=MIDDLE  ALT=\"log%282%2C16%29+%2B+log%282%2C64%29+=+log%282%2C1024%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A better way to write this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C2%5E4%29+%2B+log%282%2C2%5E6%29+=+log%282%2C2%5E10%29 ALIGN=MIDDLE  ALT=\"log%282%2C2%5E4%29+%2B+log%282%2C2%5E6%29+=+log%282%2C2%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Aha! Add the exponents<BR>\n" );
document.write( "These can be brain-twisters, and it helps if you've<BR>\n" );
document.write( "wrestled aligators, but there's no easy way out. </SPAN>\n" );
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