document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95209>Question 95209</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618052852/algebrahomeworkh>Precalculus </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> what is the 6th root of t^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69299 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=69299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Taking the 6th root of something is the same as raising it to the power or exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So taking the 6th root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as raising it to the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "This can be written as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%5E2%29%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"%28t%5E2%29%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can apply the power rule of exponents. This rule says that when you have a term with<BR>\n" );
document.write( "an exponent and you raise that term to an exponent, you multiply the two exponents.<BR>\n" );
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document.write( "In this case, when you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%5E2%29%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"%28t%5E2%29%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you multiply the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the product becomes the<BR>\n" );
document.write( "new exponent for t. <BR>\n" );
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document.write( "So we have as the new exponent for t the product: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%281%2F6%29+=+2%2F6+=+1%2F3 ALIGN=MIDDLE  ALT=\"2%2A%281%2F6%29+=+2%2F6+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the answer<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"t%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hmm. It appears as if the 1 in the numerator of the exponent is clipped off a little.<BR>\n" );
document.write( "Hopefully this doesn't confuse you. But this exponent of 1/3 just tells you to find the <BR>\n" );
document.write( "third root (or cube root) of t. And this can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+t%29 ALIGN=MIDDLE  ALT=\"root%283%2C+t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem along with providing you some information<BR>\n" );
document.write( "about the meaning of fractional exponents and how to apply the power rule for exponents.  </SPAN>\n" );
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