document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886150>Question 886150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is answer to (x-5)^(2/3)=9   With 2/3 being a fractional exponent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535737 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=535737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> BIG difference.<BR>\n" );
document.write( "x = -22 and 32 are your solutions.<BR>\n" );
document.write( "here's why:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-5)^(2/3)= 9 is the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-5)^(2/3) is the same as ((x-5)^2)^(1/3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "((x-5)^2)^(1/3) = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to get rid of the cube root, so you cube both sides of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(((x-5)^2)^(1/3))^3 = 9^3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-5)^2 = 9^3 which becomes (x-5)^2 = 729\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify (x-5)^2 by expanding it and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - 10x + 25 = 729\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 25 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - 10x - 704 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor this to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x+22) * (x-32) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get the possible solutions of:<BR>\n" );
document.write( "x = -22 or x = 32\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm your solutions are good by replacing x in the oridinal equations to see if the equations hold true.<BR>\n" );
document.write( "this step is necessary since there are problems where the possible solutions are not feasible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the original equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-5)^(2/3)= 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with -22 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(-22-5)^(2/3) = 9 which becomes (-27)^(2/3) = 9\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "(-27)^(2/3) is equivalent to either:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(-27)^2 = 729 and the cube root of 729 is eqjual to 3.<BR>\n" );
document.write( "alternatively:<BR>\n" );
document.write( "cube root of (-27) = (-3)  and (-3)^2 = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with 32 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "((32-5)^(2/3) = 9 which becomes ((27)^(2/3) = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "27 squared = 729 and the cube root of 729 is equal to 9<BR>\n" );
document.write( "alternatively:<BR>\n" );
document.write( "cube root of 27 = 3 and 3 squared = 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "looks like both solutions are good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i graphed the equation of y = (x-5)^(2/3) and the equation of y = 9 to confirm graphically that this is true.<BR>\n" );
document.write( "in the graph, you can see the intersection points of the 2 equations are at x = -22 and x = 32.<BR>\n" );
document.write( "that confirms the solution is correct graphically.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jul1001.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );