document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202433>Question 202433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can ANYONE help me with ANY of these?<BR>\n" );
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document.write( "1) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "3*4^0 = ____ <BR>\n" );
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document.write( "2) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "1 / 4^-2 = ____<BR>\n" );
document.write( "  \r<BR>\n" );
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document.write( "3) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "(1/4)^-1/2 = _____<BR>\n" );
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document.write( "4) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "(bm)^-3 = ____\r<BR>\n" );
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document.write( "5) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "y^-5 / y^-2 = ____\r<BR>\n" );
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document.write( "6) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "(-243)^3/5 = ____<BR>\n" );
document.write( "  \r<BR>\n" );
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document.write( "7) Use the rules of exponents to evaluate or simplify. Write without negative exponents.\r<BR>\n" );
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document.write( "36^1/2 = ____\r<BR>\n" );
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document.write( "Thank you for your help,<BR>\n" );
document.write( "Sarah </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152688 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=152688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's review the rules of exponents. In these rules, the \"variables\" stand for any expression (unless there is a note to the contrary). They are numbered so they can be referred to by number, <b>not</b> because any of them are more important or useful than another.)<ol><li>A power of a power: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5En%29%5Em+=+a%5E%28n%2Am%29 ALIGN=MIDDLE  ALT=\"%28a%5En%29%5Em+=+a%5E%28n%2Am%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>Multiplication with the same base: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5En+%2A+a%5Em+=+a%5E%28n+%2B+m%29 ALIGN=MIDDLE  ALT=\"a%5En+%2A+a%5Em+=+a%5E%28n+%2B+m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Pay close attention to the difference between this rule and rule #1!)</li><li>Division with the same base: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5En%29%2F%28a%5Em%29+=+a%5E%28n+-+m%29 ALIGN=MIDDLE  ALT=\"%28a%5En%29%2F%28a%5Em%29+=+a%5E%28n+-+m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>Negative exponents: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28-n%29+=+1%2F%28a%5En%29 ALIGN=MIDDLE  ALT=\"a%5E%28-n%29+=+1%2F%28a%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28a%5E%28-n%29%29+=+a%5En ALIGN=MIDDLE  ALT=\"1%2F%28a%5E%28-n%29%29+=+a%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28-n%29 ALIGN=MIDDLE  ALT=\"a%5E%28-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > stands for the reciprocal of a^n.</li><li>Zero exponents: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E0+=+1 ALIGN=MIDDLE  ALT=\"a%5E0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Note: a must <b>not</b> be zero!</li><li>Fractional exponents (where \"n\" and \"m\" are positive integers):<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2Fn%29+=++root%28n%2C+a%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2Fn%29+=++root%28n%2C+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F2%29+=+sqrt%28a%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F2%29+=+sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F3%29+=+root%283%2C+a%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F3%29+=+root%283%2C+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F4%29+=+root%284%2C+a%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F4%29+=+root%284%2C+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , etc.}}}</li><li>Using the above rule and rule #1 together: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28n%2Fm%29+=+%28+root%28m%2C+a%29%29%5En+=+root%28m%2C+a%5En%29 ALIGN=MIDDLE  ALT=\"a%5E%28n%2Fm%29+=+%28+root%28m%2C+a%29%29%5En+=+root%28m%2C+a%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul><li>The pseudo-distributive property. <b>This property is not the distributive property</b> but it does look a little like the distributive property: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Ab%29%5En+=+a%5En%2Ab%5En ALIGN=MIDDLE  ALT=\"%28a%2Ab%29%5En+=+a%5En%2Ab%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>Exponents apply only to what is <b>immediately</b> in front of them! If the symbol immediately in front of an exponent is a grouping symbol, then the exponent is applied to the entire expression in the grouping symbol. Examples:<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+=+4%2A4 ALIGN=MIDDLE  ALT=\"4%5E2+=+4%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%5E2+=+-%284%2A4%29+=+-16 ALIGN=MIDDLE  ALT=\"-4%5E2+=+-%284%2A4%29+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E2+=+%28-4%29%2A%28-4%29+=+16 ALIGN=MIDDLE  ALT=\"%28-4%29%5E2+=+%28-4%29%2A%28-4%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note the difference between this example and the previous one. Here a \")\" is right in front of the exponent. So the exponent applies to everything in the parentheses. In the previous example, a \"4\" is right in front of the exponent. So the exponent applies only to the 4 (and not the \"-\"!)</li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3%5E2+=+x+%2B+3%2A3+=+x+%2B+9 ALIGN=MIDDLE  ALT=\"x+%2B+3%5E2+=+x+%2B+3%2A3+=+x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29%5E2+=+%28x+%2B+3%29%2A%28x+%2B+3%29+=+x%5E2+%2B6x+%2B9 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%5E2+=+%28x+%2B+3%29%2A%28x+%2B+3%29+=+x%5E2+%2B6x+%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul></li></ol><BR>\n" );
document.write( "Now let's try to solve your problems.<BR>\n" );
document.write( "1) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "3*4^0 = ____<BR>\n" );
document.write( "According to PEMDAS (the order of operations) we need to simplify the exponent before doing the multiplication. So we need to figure out 4^0 first. Using rule #5 we find that 4^0 = 1. Substituting this in we get<BR>\n" );
document.write( "3*1 = ____<BR>\n" );
document.write( "which, of course, is 3.<br>\r<BR>\n" );
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document.write( "2) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "1 / 4^-2 = ____<BR>\n" );
document.write( "Using the 2nd variation of rule #4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%284%5E%28-2%29%29+=+4%5E2+=+16 ALIGN=MIDDLE  ALT=\"1%2F%284%5E%28-2%29%29+=+4%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( "3) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "(1/4)^-1/2 = _____<BR>\n" );
document.write( "Using rule #1, in \"reverse\", we can rewrite this as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F4%29%5E%28-1%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%281%2F4%29%5E%28-1%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, using rule #4, the expression in the parentheses can be simplified: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%5E%28-1%29+=+4%5E1+=+4 ALIGN=MIDDLE  ALT=\"%281%2F4%29%5E%28-1%29+=+4%5E1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%284%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which, according to rule #6, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+2 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( "4) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "(bm)^-3 = ____<BR>\n" );
document.write( "Using rule #1 again we can rewrite this as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28bm%29%5E3%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%28%28bm%29%5E3%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using rule 7:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E3%2Am%5E3%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%28b%5E3%2Am%5E3%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using rule #4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28b%5E3%2Am%5E3%29 ALIGN=MIDDLE  ALT=\"1%2F%28b%5E3%2Am%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( "5) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "y^-5 / y^-2 = ____<BR>\n" );
document.write( "Using rule #3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E%28-5%29%2F%28y%5E%28-2%29%29+=+y%5E%28%28-5+-+%28-2%29%29%29+=+y%5E%28-3%29 ALIGN=MIDDLE  ALT=\"y%5E%28-5%29%2F%28y%5E%28-2%29%29+=+y%5E%28%28-5+-+%28-2%29%29%29+=+y%5E%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using rule #4 we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E%28-3%29+=+1%2Fy%5E3 ALIGN=MIDDLE  ALT=\"y%5E%28-3%29+=+1%2Fy%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( "6) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "(-243)^3/5 = ____<BR>\n" );
document.write( "Using the second variation of rule #6:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-243%29%5E%283%2F5%29+=+%28root%285%2C+-243%29%29%5E3 ALIGN=MIDDLE  ALT=\"%28-243%29%5E%283%2F5%29+=+%28root%285%2C+-243%29%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E5+=+-243 ALIGN=MIDDLE  ALT=\"%28-3%29%5E5+=+-243\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2C+-243%29+=+-3 ALIGN=MIDDLE  ALT=\"root%285%2C+-243%29+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting into the above we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E3+=+-27 ALIGN=MIDDLE  ALT=\"%28-3%29%5E3+=+-27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( "7) Use the rules of exponents to evaluate or simplify. Write without negative exponents.<BR>\n" );
document.write( "36^1/2 = ____<BR>\n" );
document.write( "Using rule #6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%5E%281%2F2%29+=+sqrt%2836%29+=+6 ALIGN=MIDDLE  ALT=\"36%5E%281%2F2%29+=+sqrt%2836%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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