document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=838918>Question 838918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 27 to the power x  multiply by 9 to the power x+1 all divided by 3 to the power 5x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505429 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=505429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 27^x * 9^(x+1) divided by 3^(5x+3)\r<BR>\n" );
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document.write( "27^x is equal to (3*3*3)^x which is equal to (3^3)^x which is equal to 3^3x\r<BR>\n" );
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document.write( "9^(x+1) is equal to (3*3)^(x+1) which is equal to (3^2)^(x+1) which is equal to 3^(2*(x+1) which is equal to 3^(2x+2)\r<BR>\n" );
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document.write( "3^(5x+3) is ok the way it is.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "3^3x * 3^(2x+2) divided by 3^(5x+3)\r<BR>\n" );
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document.write( "3^3x * 3^(2x+2) is equal to 3^(3x + 2x+2) which is equal to 3^(5x+2)\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "3^(5x+2) divided by 3^(5x+3)\r<BR>\n" );
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document.write( "this is equal to 3^((5x+2) - (5x+3)) which is equal to 3^(5x+2-5x-3) which is equal to 3^(-1) which is equal to 1 divided by 3^1) which is equal to 1 divided by 3.\r<BR>\n" );
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document.write( "your answer is 1/3.\r<BR>\n" );
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document.write( "you can easily check whether this is correct by giving x any value and then replacing x in the original equation by its value and then evaluating the expression.\r<BR>\n" );
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document.write( "since x drops out of the equation after simplification, you should always get 1/3 as your answer if we did this correctly.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "your original expression is:\r<BR>\n" );
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document.write( "27 to the power x  multiply by 9 to the power x+1 all divided by 3 to the power 5x+3.\r<BR>\n" );
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document.write( "replace x with 2.\r<BR>\n" );
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document.write( "your original expression becomes:\r<BR>\n" );
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document.write( "27 to the power of 2 multiply by 9 to the power of (2+1) all divided by 3 to the power of (5*2 + 3)\r<BR>\n" );
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document.write( "this simplifies to:\r<BR>\n" );
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document.write( "27 to the power of 2 multiply by 9 to the power of 3 all divided by 3 to the power of 13.\r<BR>\n" );
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document.write( "simplifying that further, you get:\r<BR>\n" );
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document.write( "729 * 729 all divided by 1594323.\r<BR>\n" );
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document.write( "simplifying that further, you get:\r<BR>\n" );
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document.write( "531441 divided by 1594323.\r<BR>\n" );
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document.write( "since 531441 divides into 1594323 exactly three times, this simplifies to:\r<BR>\n" );
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document.write( "1/3.\r<BR>\n" );
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document.write( "solution is confirmed as good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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