document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118977>Question 1118977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression and express your answer using positive exponents only. <BR>\n" );
document.write( "(3^2xy^-1)^-2(6x^-4y^3)(9x^3y^-2)^3/(3x^-3y^-4)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734410 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are all kinds of different sequences of steps you could take to simplify an expression like this.  For someone just learning about problems like this, I would probably suggest the following:<BR>\n" );
document.write( "(1) simplify the \"3^2\"<BR>\n" );
document.write( "(2) wherever an expression in parentheses is raised to a power, \"distribute\" the exponent to the factors inside the parentheses<BR>\n" );
document.write( "(3) simplify the coefficient (the numerical part of the answer)<BR>\n" );
document.write( "(4) wherever that leaves you with a negative exponent, move that factor to the denominator if it is in the numerator, or move it to the numerator if it is in the denominator<BR>\n" );
document.write( "(5) combine exponents on each variable in the numerator and denominator<BR>\n" );
document.write( "(6) cancel factors where needed to end up with an expression containing each variable only once and with a positive exponent<br><BR>\n" );
document.write( "Again, there are numerous variations on the sequence of steps you can take to perform the simplification.<br><BR>\n" );
document.write( "If you are thoroughly familiar with the process of simplifying expressions like these, you can accomplish all but the last step in a single step:<br><BR>\n" );
document.write( "in the numerator...<BR>\n" );
document.write( ".. (3^2)^-2) gives 9^-2, which gives me a 9^2 in the denominator<BR>\n" );
document.write( ".. x^-2 gives me an x^2 in the denominator<BR>\n" );
document.write( ".. (y^-1)^-2 gives me a y^2 in the numerator<BR>\n" );
document.write( ".. the 6 stays in the numerator<BR>\n" );
document.write( ".. (x^-4) gives me an x^4 in the denominator<BR>\n" );
document.write( ".. the y^3 stays in the numerator<BR>\n" );
document.write( ".. the 9^3 stays in the numerator<BR>\n" );
document.write( ".. the (x^3)^3 gives me an x^9 in the numerator<BR>\n" );
document.write( ".. the (y^-2)^3 gives y^-6, which gives me a y^6 in the denominator<br><BR>\n" );
document.write( "in the denominator...<BR>\n" );
document.write( ".. 3^2 gives me 9, which stays in the denominator<BR>\n" );
document.write( "..(x^-3)^2 gives me x^-6, which gives me an x^6 in the numerator<BR>\n" );
document.write( "..(y^-4)^2 gives me y^-8, which gives me a y^8 in the numerator<br><BR>\n" );
document.write( "And now write all the factors in their proper places...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2%29%286%29%28y%5E3%29%289%5E3%29%28x%5E9%29%28x%5E6%29%28y%5E8%29%29%2F%28%289%5E2%29%28x%5E2%29%28x%5E4%29%28y%5E6%29%289%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simplify the coefficient and combine exponents in the numerator and denominator...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%28x%5E15%29%28y%5E13%29%29%2F%28%28x%5E6%29%28y%5E6%29%29 ALIGN=MIDDLE  ALT=\"%286%28x%5E15%29%28y%5E13%29%29%2F%28%28x%5E6%29%28y%5E6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and simplify...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28x%5E9%29%28y%5E7%29 ALIGN=MIDDLE  ALT=\"6%28x%5E9%29%28y%5E7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );