document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78765>Question 78765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CAN SOMEONE HELP ME WITH THIS, PLEASE?\r<BR>\n" );
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document.write( "Simplify.  Assume x represents a positive number.<BR>\n" );
document.write( "SQURT.80X^4\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 #56507 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><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=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=56507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28.8x%5E4%29 ALIGN=MIDDLE  ALT=\"sqrt%28.8x%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first thing I see from this is that you can pull the x^4 term out from under<BR>\n" );
document.write( "the radical and get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2sqrt%280.8%29 ALIGN=MIDDLE  ALT=\"x%5E2sqrt%280.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Do you understand why that can be done? Think about it this way:<BR>\n" );
document.write( "When you take the square root of a number, you are really raising<BR>\n" );
document.write( "that number to the 1/2 power, like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E4%29=%28x%5E4%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E4%29=%28x%5E4%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is a property about exponents that when a number with an exponent is raised <BR>\n" );
document.write( "to another exponent, it can be simplified by keeping the base number and multiplying the exponents. In other words:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%5E%281%2F2%29=x%5E%284%2A%281%2F2%29%29=x%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%5E%281%2F2%29=x%5E%284%2A%281%2F2%29%29=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So that is how I was justified in getting the x^4 out from under the radical as an x^2.<BR>\n" );
document.write( "You can now simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2sqrt%280.8%29 ALIGN=MIDDLE  ALT=\"x%5E2sqrt%280.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > even more if you recognize that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.8=0.2%2A0.2%2A2%2A2%2A5 ALIGN=MIDDLE  ALT=\"0.8=0.2%2A0.2%2A2%2A2%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the same logic as above, I can pull out a 0.2 and a 2 from under the radical. This leaves you with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2%2A2x%5E2sqrt%285%29 ALIGN=MIDDLE  ALT=\"0.2%2A2x%5E2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4x%5E2sqrt%285%29 ALIGN=MIDDLE  ALT=\"0.4x%5E2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It's open to debate if that final answer is simpler than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2sqrt%280.8%29 ALIGN=MIDDLE  ALT=\"x%5E2sqrt%280.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "but at least it is good practice in dealing with radicals!\r<BR>\n" );
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document.write( "Good Luck,<BR>\n" );
document.write( "tutor_paul@yahoo.com </SPAN>\n" );
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