document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=383778>Question 383778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4^&#8730;243x^8y^10 my answer was (6x^3y^5)^4&#8730;3x^2 but the answer in my math book is (3x^2y^2)4^&#8730;3y^2 what am i doing work here? please help me. thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271697 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=271697\">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=root%284%2C+243x%5E8y%5E10%29 ALIGN=MIDDLE  ALT=\"root%284%2C+243x%5E8y%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'm not sure I can figure out how you got the answer you did. So I will not be able to explain what went wrong. But your Math book is correct.<br><BR>\n" );
document.write( "Your expression is a 4th root. And to simplify a 4th root you look for factors of the radicand (the expression within the radical) that are 4th powers. (Other factors are of no real interest.)<br><BR>\n" );
document.write( "For 243 there may be many ways to factor it but one way, 81*3, involves a factor that is a 4th power. (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81+=+3%5E4 ALIGN=MIDDLE  ALT=\"81+=+3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) For the variables we factor each one into as many powers of 4 as we can. Putting all these factors together we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+3%5E4%2A3%2Ax%5E4%2Ax%5E4%2Ay%5E4%2Ay%5E4%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"root%284%2C+3%5E4%2A3%2Ax%5E4%2Ax%5E4%2Ay%5E4%2Ay%5E4%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take a moment to make sure you see how your original radicand and the factored one you see above are equal to each other.<br><BR>\n" );
document.write( "Next, I like to use the Commutative Property of Multiplication to reorder the factors so that all the 4th powers are in front:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+3%5E4%2Ax%5E4%2Ax%5E4%2Ay%5E4%2Ay%5E4%2A3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"root%284%2C+3%5E4%2Ax%5E4%2Ax%5E4%2Ay%5E4%2Ay%5E4%2A3%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we use a property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to separate all the 4th power factors into their own radicals. (The factors that are not 4th powers (at the end) just stay all in the same radical.):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+3%5E4%29%2Aroot%284%2C+x%5E4%29%2Aroot%284%2C+x%5E4%29%2Aroot%284%2C+y%5E4%29%2Aroot%284%2C+y%5E4%29%2Aroot%284%2C+3%2Ay%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now all the 4th roots of the 4th powers simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%2Ax%2Ay%2Ay%2Aroot%284%2C+3y%5E2%29 ALIGN=MIDDLE  ALT=\"3%2Ax%2Ax%2Ay%2Ay%2Aroot%284%2C+3y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2Ay%5E2%2Aroot%284%2C+3y%5E2%29 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2Ay%5E2%2Aroot%284%2C+3y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is the answer in your book. </SPAN>\n" );
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