document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094495>Question 1094495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the value of (p+q+r); if p,q, and r are positive integers, p^q = 8, and r^(1/p) = 7\r<BR>\n" );
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document.write( "This is what I tried but my answer doesn't match the answer key. Please see below:\r<BR>\n" );
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document.write( "p^q = 8 => 2^3 = 8\r<BR>\n" );
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document.write( "p = 2 and q = 3\r<BR>\n" );
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document.write( "Replacing the equation r^(1/p) = 7 with p gives me this:\r<BR>\n" );
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document.write( "r^(1/2) = 7\r<BR>\n" );
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document.write( "To make this equation true I assumed that the value of r should be 7:<BR>\n" );
document.write( "7^(1/2) = 7<BR>\n" );
document.write( "7 = 7\r<BR>\n" );
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document.write( "So, p+q+r = 2+3+7 = 12 but my answer key contains different answer. Please help.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709086 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=709086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "You have p = 2 and q = 3 correct. <BR>\n" );
document.write( "p^q = 2^3 = 8 is true\r<BR>\n" );
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document.write( "If r^(1/p) = 7, then r^(1/2) = 7 meaning that r = 49 (not r = 7)<BR>\n" );
document.write( "You square both sides to get rid of the exponent of 1/2 as shown below\r<BR>\n" );
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document.write( "r^(1/2) = 7<BR>\n" );
document.write( "[ r^(1/2) ] ^2  = 7^2<BR>\n" );
document.write( "r^(1/2*2)  = 49<BR>\n" );
document.write( "r^(2/2)  = 49<BR>\n" );
document.write( "r^1  = 49<BR>\n" );
document.write( "r  = 49\r<BR>\n" );
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document.write( "So in summary: <BR>\n" );
document.write( "p = 2, q = 3, r = 49\r<BR>\n" );
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document.write( "Making<BR>\n" );
document.write( "p+q+r = 2+3+49 = 5+49 = <font color=red size=4>54</font> which is the answer.\r<BR>\n" );
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document.write( "-----------------------------\r<BR>\n" );
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document.write( "Side Note: exponents of 1/2 indicate square root. So for example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%281%2F2%29%5E%22%22+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"x%5E%281%2F2%29%5E%22%22+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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