document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74025>Question 74025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i sove this equation?\r<BR>\n" );
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document.write( "(x^2)^-3(x^-2)<BR>\n" );
document.write( "over<BR>\n" );
document.write( "(x^2)^-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53028 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=53028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(x^2)^{-3}(x^{-2})}{(x^2)^{-4}\"><BR>\n" );
document.write( "When you raise a base with an exponent to an exponent you multiply the exponents (ie <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x^y)^z=x^{y*z}\">). For instance <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x^2)^{-4}=x^{2*(-4)}=x^{-8}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(x)^{-3*2}(x^{-2})}{(x)^{-4*2}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(x)^{-6}(x^{-2})}{(x)^{-8}\"><BR>\n" );
document.write( "When you multiply like bases with exponents, you add the exponents (ie <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2*x^2=x^{2+2}=x^4\">)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(x)^{-6+(-2)}}{(x)^{-8}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(x)^{-8}}{(x)^{-8}\">Multiply the numerator by adding the exponents<BR>\n" );
document.write( "When you divide like bases with exponents, you subtract the exponents (ie <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x^2}{x^2}=x^{2-2}=x^0=1\">)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x)^{-8-(-8)}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x)^{-8+8)}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x)^{0}=1\"><BR>\n" );
document.write( "After all of that, we get an answer of 1. This means that for any value of x, I should get 1 everytime<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Let x equal any number. Lets make x equal to 2 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(x^2)^{-3}(x^{-2})}{(x^2)^{-4}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(2^2)^{-3}(2^{-2})}{(2^2)^{-4}\">Plug in x=2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{(4)^{-3}(\frac{1}{4})}{(4)^{-4}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\frac{1}{4^3}(\frac{1}{4})}{\frac{1}{4^4}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\frac{1}{64}(\frac{1}{4})}{\frac{1}{256}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\frac{1}{256}}{\frac{1}{256}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{\not{256}}\frac{\not{256}}{1}=1\">These cancel<BR>\n" );
document.write( "If you want more proof, let x equal any other number and you will get 1. Hope this makes sense. </SPAN>\n" );
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