document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70148>Question 70148</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132203138/algebrahomeworkh>College Algebra Essentials</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> (x - 4)2/3 power = 16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50088 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=50088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E%282%2F3%29+=+16 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E%282%2F3%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cube both sides.  In the case of the left side that means multiplying it by itself so that<BR>\n" );
document.write( "the multiplications are:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E%282%2F3%29%2A%28x-4%29%5E%282%2F3%29%2A%28x-4%29%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E%282%2F3%29%2A%28x-4%29%5E%282%2F3%29%2A%28x-4%29%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But when you multiply a base term [in this case the base is (x-4)] that has an exponent by<BR>\n" );
document.write( "the same base term with other exponents, the product is the same base term, but the new<BR>\n" );
document.write( "exponent is the sum of the exponents.  For example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Ea+%2Ax%5Eb%2Ax%5Ec=+x%5E%28a%2Bb%2Bc%29 ALIGN=MIDDLE  ALT=\"x%5Ea+%2Ax%5Eb%2Ax%5Ec=+x%5E%28a%2Bb%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the case of taking the cube of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the product will be<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E%28%282%2F3%29%2B%282%2F3%29%2B%282%2F3%29%29+=+%28x-4%29%5E%286%2F3%29+=+%28x-4%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That is it cube of the left side of the original problem.  And since we cubed the left<BR>\n" );
document.write( "side, we must also cube the right side.  16 cubed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A16%2A16 ALIGN=MIDDLE  ALT=\"16%2A16%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "We have now converted the original problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2+=+16%2A16%2A16 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2+=+16%2A16%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now take the square root of both sides.  The left side becomes just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4 ALIGN=MIDDLE  ALT=\"x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The first<BR>\n" );
document.write( "two terms on the right side are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A16 ALIGN=MIDDLE  ALT=\"16%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2 ALIGN=MIDDLE  ALT=\"16%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This gets multiplied by the remaining 16 to become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%5E2%29%2A16 ALIGN=MIDDLE  ALT=\"%2816%5E2%29%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you now take the square root of this product you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2816%5E2%29%2A16%29+=+sqrt%2816%5E2%29%2Asqrt%2816%29+=+16%2A4+=+64 ALIGN=MIDDLE  ALT=\"sqrt%28%2816%5E2%29%2A16%29+=+sqrt%2816%5E2%29%2Asqrt%2816%29+=+16%2A4+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting this in to expression results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4+=+64 ALIGN=MIDDLE  ALT=\"x-4+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, add 4 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+68 ALIGN=MIDDLE  ALT=\"x+=+68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I hope you are able to follow all the detail. You can check the answer by substituting<BR>\n" );
document.write( "this value for x into the original problem so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4 ALIGN=MIDDLE  ALT=\"x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes 64.  Then  find the<BR>\n" );
document.write( "cube root of 64 and square it.  Or you may opt to square 64 and take the cube root of<BR>\n" );
document.write( "that number.  In both cases you should get 16, the same number as on the right side of<BR>\n" );
document.write( "the original problem statement.    </SPAN>\n" );
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