document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241289>Question 241289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sqrt(8a^9)/b^3 = (8a^9)(b^3)<BR>\n" );
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document.write( "               =  (8a^3)(b^3)\r<BR>\n" );
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document.write( "               = 8ab^3\r<BR>\n" );
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document.write( "Is this correct?  I am not sure I am following the steps correctly in this formula? \r<BR>\n" );
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document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176702 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=176702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288a%5E9%29%2Fb%5E3+=+%288a%5E9%29%2A%28b%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%288a%5E9%29%2Fb%5E3+=+%288a%5E9%29%2A%28b%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since b^3 * b^3 = b^(3+3), then multiply both sides of equation by b^3 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288a%5E9%29+=+%288a%5E9%29%2A%28b%5E6%29 ALIGN=MIDDLE  ALT=\"sqrt%288a%5E9%29+=+%288a%5E9%29%2A%28b%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "divide both sides of your equation by b^9 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%288a%5E9%29%29+%2F+%288a%5E9%29+=+%28b%5E6%29 ALIGN=MIDDLE  ALT=\"%28sqrt%288a%5E9%29%29+%2F+%288a%5E9%29+=+%28b%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since sqrt(8a^9)^2 = 8a^9, and (8a^9)^2 = 64a^18, and (b^6)^2 = b^12, then square both sides of your equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288a%5E9%29+%2F+%2864a%5E18%29+=+%28b%5E12%29 ALIGN=MIDDLE  ALT=\"%288a%5E9%29+%2F+%2864a%5E18%29+=+%28b%5E12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since 8/64 = 1/8, and a^9 / a^18 = a^(9-18) = a^(-9) = 1/a^9, then perform the indicated operations to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%288a%5E9%29%29+=+%28b%5E12%29 ALIGN=MIDDLE  ALT=\"%281%2F%288a%5E9%29%29+=+%28b%5E12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you are solving for b, then you will get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+root%2812%2C%281%2F%288a%5E9%29%29%29 ALIGN=MIDDLE  ALT=\"b+=+root%2812%2C%281%2F%288a%5E9%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you are solving for a, then you will get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+root%289%2C%28%281%2Fb%5E12%29%2F8%29%29 ALIGN=MIDDLE  ALT=\"a+=+root%289%2C%28%281%2Fb%5E12%29%2F8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I confirmed the answer is good by letting a = 2.\r<BR>\n" );
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document.write( "This made b = .5\r<BR>\n" );
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document.write( "You can confirm for yourself by using any number for a and then solving for b.\r<BR>\n" );
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document.write( "conversely  you can use any number for b and then solve for a.\r<BR>\n" );
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document.write( "either way, the answers should be able to be plugged into the original equation to confirm that the values are good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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