document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175709>Question 1175709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the exponential form  of the expression:\r<BR>\n" );
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document.write( "cube root of 125t^3d^7.<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 #801365 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the expression, as i understand it, is:\r<BR>\n" );
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document.write( "125 * t^3 * d^7\r<BR>\n" );
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document.write( "you want to take the cube root of that expression.\r<BR>\n" );
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document.write( "the expression becomes:\r<BR>\n" );
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document.write( "(125 * t^3 * d^7) ^ (1/3)\r<BR>\n" );
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document.write( "this simplified as:\r<BR>\n" );
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document.write( "125^(1/3) * (t^3)^(1/3) * (d^7)^(1/3).\r<BR>\n" );
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document.write( "that simplifies to:\r<BR>\n" );
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document.write( "5 * t * d^(7/3)\r<BR>\n" );
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document.write( "you can confirm this is true by assigning random values to t and d and evalucating both the original expression and the final expression.\r<BR>\n" );
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document.write( "if they yield the same answer, then there is a high probability that the conversion was done successfully.\r<BR>\n" );
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document.write( "i used 7 for t and 4 for d and evaluated the original expression and the final expression and determined they were the same.\\r<BR>\n" );
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document.write( "this confirmed the conversion was correct and that the original expression and the final expression were equivalent.\r<BR>\n" );
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document.write( "in general, the exponential form of the cube root funcion is the value under the cube root sign raised to the 1/3 power.\r<BR>\n" );
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document.write( "example, cube root of 125 is equal to 5 becomes 5 ^ 3 = 125.\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L1_T3_text_final.html\" target = \"_blank\">http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L1_T3_text_final.html</a>\r<BR>\n" );
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