document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=864565>Question 864565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%5E%284x%2B1%29+%2A+4%5E4+%2A+5%5E%282x%2B2%29%29+%2F+%2881%5E%28x-1%29+%2A+2%5E3+%2A+25%5Ex%29+=+3%5Ea+%2A+6%5Eb+%2A+10%5Ec++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > find the integer value of a + b + c </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521105 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=521105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (3^(4x+1) * 4^4 * 5^(2x+2)) / (81^(x-1) * 2^3 * 25^x) =194400<BR>\n" );
document.write( "194400 =3^a * 6^b * 10^c<BR>\n" );
document.write( "194400 =2^5×3^5×5^2 prime factors\r<BR>\n" );
document.write( "\n" );
document.write( "first take out all 10's =5 and matching 2<BR>\n" );
document.write( "2*2×5*5=10^2<BR>\n" );
document.write( "next take out all 2's and matching 3's ie 6's<BR>\n" );
document.write( "3*3×3*2*2*2=6^3<BR>\n" );
document.write( "and remaining 3's<BR>\n" );
document.write( "3*3=3^2\r<BR>\n" );
document.write( "\n" );
document.write( "(3^(4x+1) * 4^4 * 5^(2x+2)) / (81^(x-1) * 2^3 * 25^x) =3^2*6^3*10^2<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "c=2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );