document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093853>Question 1093853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help with the following :<BR>\n" );
document.write( "Simplify the expression. Use positive exponent only: (4&#119909;^&#8722;1)^2(2&#119909;^3)^3 \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 #708463 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=708463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i see this problem as:\r<BR>\n" );
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document.write( "(4x^(-1))^2 * (2x^3)^3\r<BR>\n" );
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document.write( "this is equal to 4^2 * x^(-2) * 2^3 * x^9\r<BR>\n" );
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document.write( "rearrange the terms to get 4^2 * 2^3 * x^(-2) * x^9\r<BR>\n" );
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document.write( "simplify further to get 128 * x^(-2) * x^9\r<BR>\n" );
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document.write( "combine like terms to get 128 * x^7\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "you can confirm using your calculator by evaluating the original expression and the final expression using a random value of x.\r<BR>\n" );
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document.write( "if the answer comes out the same, then you did good.\r<BR>\n" );
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document.write( "i used x = 25 and i got both expressions equal to 7.8125 * 10^11, so i think i did good.\r<BR>\n" );
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document.write( "breaking it down, this is what was involved.\r<BR>\n" );
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document.write( "(4x^-1)^2 is equal to 4^2 * (x^-1)^2 which is equal to 4^2 * x^(-1*2) which is equal to 4^2 * x^(-2)\r<BR>\n" );
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document.write( "the exponent arithmetic properties that are involved are:\r<BR>\n" );
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document.write( "(x^a)^b is equal to x^(a*b).\r<BR>\n" );
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document.write( "(x^a * y^b) ^ c is equal to x^(a*c) * y^(b*c).\r<BR>\n" );
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document.write( "the same properties apply to (2x^3)^3.\r<BR>\n" );
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document.write( "that is equal to 2^3 * (x^3)^3 which is equal to 2^3 * x^(3*3) which is equal to 2^3 * x^9.\r<BR>\n" );
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document.write( "you were then left with:\r<BR>\n" );
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document.write( "4^2 * x^(-2) * 2^3 * x^9\r<BR>\n" );
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document.write( "the other property of exponents involved is:\r<BR>\n" );
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document.write( "x^a * x^b is equal to x^(a + b) and:\r<BR>\n" );
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document.write( "x^a / x^b is equal to x^(a-b)\r<BR>\n" );
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document.write( "there's another property that states:\r<BR>\n" );
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document.write( "x^(-a) is equal to 1/x^a.\r<BR>\n" );
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document.write( "your expression of 4^2 * x^(-2) * 2^3 * x^9 becomes:\r<BR>\n" );
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document.write( "4^2 * 2^3 * x^9 * x^-2)\r<BR>\n" );
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document.write( "simplifying and using the properties of exponents, you get:\r<BR>\n" );
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document.write( "4^2 * x^(-2) * 2^3 * x^9 becomes 16 * x^(9-2) * 8 which becomes 128 * x^7.\r<BR>\n" );
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document.write( "here's some good references on exponent arithmetic that you might find useful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm</a>\r<BR>\n" );
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document.write( "let me know if you have any further questions regarding this.\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
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