document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22386>Question 22386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain how you use the 5 rules of exponents to simplify the following expressions. Do not leave any negative exponents in your answer.: <BR>\n" );
document.write( "a. (x^10 · y^3)/(x^4 · y^5) <BR>\n" );
document.write( "b. [(p^4 · q^5)/(r^3)]^2 <BR>\n" );
document.write( "c. (108r^2 · y)/(9r^3 · y^2) <BR>\n" );
document.write( "d. (3x^2 · y^2) · (-5x · y^4)^2 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11679 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E10+%2A+y%5E3%29%2F%28x%5E4+%2A+y%5E5%29+ ALIGN=MIDDLE  ALT=\"%28x%5E10+%2A+y%5E3%29%2F%28x%5E4+%2A+y%5E5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you divide with the same base number, you subtract exponents.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6%2Ay%5E%28-2%29 ALIGN=MIDDLE  ALT=\"x%5E6%2Ay%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "When you have a negative exponent such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E%28-2%29 ALIGN=MIDDLE  ALT=\"y%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > it becomes a fraction whose numerator is 1, and the denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28y%5E2%29+ ALIGN=MIDDLE  ALT=\"1%2F%28y%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6+%2A%281%2F%28y%5E2%29%29+ ALIGN=MIDDLE  ALT=\"x%5E6+%2A%281%2F%28y%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E6%29%2F%28y%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E6%29%2F%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28p%5E4+%2A+q%5E5%29%2F%28r%5E3%29%29%5E2+ ALIGN=MIDDLE  ALT=\"%28%28p%5E4+%2A+q%5E5%29%2F%28r%5E3%29%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you raise a power to a power, you multiply the exponents:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28p%5E8+%2Aq%5E10%29%2F%28r%5E6%29+ ALIGN=MIDDLE  ALT=\"+%28p%5E8+%2Aq%5E10%29%2F%28r%5E6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28108r%5E2+%2A+y%29%2F%289r%5E3+%2A+y%5E2%29+ ALIGN=MIDDLE  ALT=\"+%28108r%5E2+%2A+y%29%2F%289r%5E3+%2A+y%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rewrite the fraction into three fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28108%2F9%29%2A%28r%5E2%2Fr%5E3%29%2A%28y%2F%28y%5E2%29%29+ ALIGN=MIDDLE  ALT=\"%28108%2F9%29%2A%28r%5E2%2Fr%5E3%29%2A%28y%2F%28y%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%29%2A%281%2Fr%29%2A+%281%2Fy%29+ ALIGN=MIDDLE  ALT=\"%2812%29%2A%281%2Fr%29%2A+%281%2Fy%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28ry%29 ALIGN=MIDDLE  ALT=\"12%2F%28ry%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2+%2A+y%5E2%29+%2A+%28-5x+%2A+y%5E4%29%5E2+ ALIGN=MIDDLE  ALT=\"%283x%5E2+%2A+y%5E2%29+%2A+%28-5x+%2A+y%5E4%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square everything in the second parentheses:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2+%2Ay%5E2%29+%2A%2825%2Ax%5E2%2Ay%5E8%29+ ALIGN=MIDDLE  ALT=\"%283x%5E2+%2Ay%5E2%29+%2A%2825%2Ax%5E2%2Ay%5E8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you multiply with the same base number, you add exponents:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75x%5E4y%5E10+ ALIGN=MIDDLE  ALT=\"75x%5E4y%5E10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( " </SPAN>\n" );
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