document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007354>Question 1007354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving (x^2 * y^3) * (x^-2 * y^-2), with ^ representing to the power to (Exponent)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623358 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the problem as you show it is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 * y^3) * (x^-2 * y^-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since they're all multiplications, you can remove the parentheses to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 * y^3 * x^-2 * y^-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can use the associative law to regroup them as shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 * x^-2) * (y^3 * y^-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 * x^-2 = x^(2-2) = x^0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y^3 * y^-2 = y^(3-2) = y^1 = y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answer is y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the exponent property that allows this is\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^a * x^b = x^(a+b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when a = 2 and b = -2, this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 * x^-2 = x^(2 + (-2)) which becomes x^(2-2) which becomes x^0 which is equal to 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "similarly, y^a + y^b = y^(a+b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when a = 3 and b = -2, this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y^3 * y^-2) = y^(3 + (-2)) which becomes y^(3-2) which becomes y^1 which is equal to y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "another exponent property that you could have used is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^-a = 1/x^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "also x^a / x^b = x^(a-b).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using this property, you get x^-2 = 1/x^2 and y^-2 = 1/y^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation of (x^2 * y^3) * (x^-2 * y^-2) becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 * y^3) * (1/x^2 * 1/y^2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "re-associate as before to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 * 1/x^2) * (y^3 * 1/y^2) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^(2-2) * y^(3-2) which becomes x^0 * y^1 which becomes y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get the same answer either way.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );