document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=759572>Question 759572</A>: <I><SPAN STYLE=\"word-break: break-all;\">  -8^-5/3 = -1/(8^5/3) = -1/(8^1/3)^5 = -1/32 What steps are being done between these answers?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462621 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=462621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -8^(-5/3) = -1/(8^(5/3)) = -1/(8^(1/3))^5 = -1/32<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%5E%28-5%2F3%29+=+-1%2F%28%288%5E%285%2F3%29%29%29+=+-1%2F%288%5E%281%2F3%29%29%5E5+=+-1%2F32 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first two equal signs are just the definition of negative exponent and the definition of rational exponent (with a minus sign in front of each expression).<BR>\n" );
document.write( "I cannot imagine any intermediate steps there.<BR>\n" );
document.write( "Definition of rational exponent (for positive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and positive integers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E%28m%2Fn%29=%28b%5E%281%2Fn%29%29%5Em ALIGN=MIDDLE  ALT=\"b%5E%28m%2Fn%29=%28b%5E%281%2Fn%29%29%5Em\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%28n%2Cb%29%29%5Em ALIGN=MIDDLE  ALT=\"%28root%28n%2Cb%29%29%5Em\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5Em%29%5E%281%2Fn%29 ALIGN=MIDDLE  ALT=\"%28b%5Em%29%5E%281%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Cb%5Em%29 ALIGN=MIDDLE  ALT=\"root%28n%2Cb%5Em%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I cannot imagine any intermediate steps there.<BR>\n" );
document.write( "Definition of negative exponent (for any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E%28-x%29=1%2Fb%5Ex ALIGN=MIDDLE  ALT=\"b%5E%28-x%29=1%2Fb%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The last equal sign could be explained by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=2%5E3 ALIGN=MIDDLE  ALT=\"8=2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%29=8%5E%281%2F3%29=%282%5E3%29%5E%281%2F3%29=2%5E%28%283%2A%281%2F3%29%29%29=2%5E1=2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5=32 ALIGN=MIDDLE  ALT=\"2%5E5=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You could write out more in-between steps there, but I would think that anything more than<BR>\n" );
document.write( "... = -1/(8^1/3)^5 = 1/2^5 = -1/32<BR>\n" );
document.write( "is overkill. </SPAN>\n" );
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