document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=630183>Question 630183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain why -5x² and (-5x)² are not equivalent.<BR>\n" );
document.write( "Explain why the expressions 2³ × 5³ and 10³ are equivalent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396781 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=396781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Important: Exponents only apply to what is literally in front of them!<br><BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%5E2 ALIGN=MIDDLE  ALT=\"-5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is the \"x\" that is in front of the exponent. So the exponent applies only to the x. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%5E2 ALIGN=MIDDLE  ALT=\"-5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is short for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Ax%2Ax ALIGN=MIDDLE  ALT=\"-5%2Ax%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5x%29%5E2 ALIGN=MIDDLE  ALT=\"%28-5x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is the right parenthesis that is in front of the exponent. This means that the exponent applies to the whole expression inside the parentheses. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5x%29%5E2 ALIGN=MIDDLE  ALT=\"%28-5x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is short for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5x%29%2A%28-5x%29 ALIGN=MIDDLE  ALT=\"%28-5x%29%2A%28-5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2 ALIGN=MIDDLE  ALT=\"25x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<br><BR>\n" );
document.write( "One of the rules/properties of exponents is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5En%2Ab%5En+=+%28a%2Ab%29%5En ALIGN=MIDDLE  ALT=\"a%5En%2Ab%5En+=+%28a%2Ab%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The expression<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E7%2A5%5E7 ALIGN=MIDDLE  ALT=\"2%5E7%2A5%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "matches the pattern of the left side of the rule above. So according to the rule it must be equal to the right side of the rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A5%29%5E7 ALIGN=MIDDLE  ALT=\"%282%2A5%29%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E7 ALIGN=MIDDLE  ALT=\"10%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "As usual, if you have trouble using the rules for exponents, work without them! In other words, rewrite your expressions without exponents and simplify without them.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E7%2A5%5E7 ALIGN=MIDDLE  ALT=\"2%5E7%2A5%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes<BR>\n" );
document.write( "2*2*2*2*2*2*2*5*5*5*5*5*5*5<BR>\n" );
document.write( "This is all multiplication so we can use the Commutative Property of Multiplication to change the order as we please and we can use the Associative Property of Multiplication to rearrange the grouping as we please. So we can change the above to:<BR>\n" );
document.write( "(2*5)*(2*5)*(2*5)*(2*5)*(2*5)*(2*5)*(2*5)<BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "(10)*(10)*(10)*(10)*(10)*(10)*(10)<BR>\n" );
document.write( "which can be rewritten as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E7 ALIGN=MIDDLE  ALT=\"10%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );