document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172894>Question 172894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please explain the answer to i^49?  I factor out 13*3, but cannot resolve the remaining terms...thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127748 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=127748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take note that 49 = 48 + 1 and 48 = 12*4. \r<BR>\n" );
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document.write( "Also, we'll use the identities <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez ALIGN=MIDDLE  ALT=\"x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E4=1 ALIGN=MIDDLE  ALT=\"i%5E4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E%2849%29=i%5E%2848%2B1%29=i%5E%2812%2A4%2B1%29=i%5E%2812%2A4%29i%5E1=%28i%5E4%29%5E12%2Ai=%281%29%5E12%2Ai=%281%29%2Ai=i ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E49=i ALIGN=MIDDLE  ALT=\"i%5E49=i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------------------------\r<BR>\n" );
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document.write( "If you want an easier method, do the following:\r<BR>\n" );
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document.write( "Divide the exponent 49 by 4 to get 12 remainder 1\r<BR>\n" );
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document.write( "Since the remainder is 1, this tells us that the answer is \"i\" (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E49=i ALIGN=MIDDLE  ALT=\"i%5E49=i\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "This is a handy thing to remember (or put in your reference book)\r<BR>\n" );
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document.write( "If the remainder is 0, the answer is 1<BR>\n" );
document.write( "If the remainder is 1, the answer is \"i\"<BR>\n" );
document.write( "If the remainder is 2, the answer is -1<BR>\n" );
document.write( "If the remainder is 3, the answer is \"-i\" </SPAN>\n" );
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