document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123339>Question 123339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me? I have tried working it out but it doesn't check out right.<BR>\n" );
document.write( "(x+7)^3/2=27 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90523 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=90523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The way you wrote your problem it could be interpreted in several ways. It could be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E3%2F2=27 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E3%2F2=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But I suspect that you meant:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E%283%2F2%29=27 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E%283%2F2%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So I am going to work the second version in which the exponent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If I am not correct<BR>\n" );
document.write( "you will probably need to post your problem again. <BR>\n" );
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document.write( "Starting with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E%283%2F2%29=27 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E%283%2F2%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can use the power rule of exponents to rewrite the problem as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B7%29%5E%281%2F2%29%29%5E3+=+27 ALIGN=MIDDLE  ALT=\"%28%28x%2B7%29%5E%281%2F2%29%29%5E3+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that on the right side the 27 is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3 ALIGN=MIDDLE  ALT=\"3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute 3 cubed for 27<BR>\n" );
document.write( "and the equation then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B7%29%5E%281%2F2%29%29%5E3+=+3%5E3 ALIGN=MIDDLE  ALT=\"%28%28x%2B7%29%5E%281%2F2%29%29%5E3+=+3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Take the cube root of both sides and the equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E%281%2F2%29+=+3 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E%281%2F2%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square both sides and the equation is then:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+7%29+=+9 ALIGN=MIDDLE  ALT=\"%28x+%2B+7%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 7 from both sides and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check ... return to the original problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E%283%2F2%29=27 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E%283%2F2%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 2 for 7 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B7%29%5E%283%2F2%29+=+27 ALIGN=MIDDLE  ALT=\"%282%2B7%29%5E%283%2F2%29+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the 2 + 7 to get 9 and the problem then is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%29%5E%283%2F2%29+=+27 ALIGN=MIDDLE  ALT=\"%289%29%5E%283%2F2%29+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can then take the square root of 9 and cube it or cube 9 and take the square root of that<BR>\n" );
document.write( "with the same result. The square root of 9 is 3 and if you cube 3 you get 27, making the<BR>\n" );
document.write( "equation become 27 = 27. Or you can cube 9 and get 729. Then take the square root of 729<BR>\n" );
document.write( "and get 27 ... again making the equation 27 = 27. Or, since 3/2 = 1.5, you can use a calculator<BR>\n" );
document.write( "and raise 9 to the 1.5 power and you again get 27 ... once more making the equation 27 = 27.<BR>\n" );
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document.write( "In any case x = 2 is a valid solution to the problem.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work it through to a solution.<BR>\n" );
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