document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092943>Question 1092943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the properties of exponents to simplify the expression. \r<BR>\n" );
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document.write( "(5^2)(5^-3) = \r<BR>\n" );
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document.write( "If would be great if you could please explain why the answer is 1/5.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707566 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=707566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5^2 * 5^-3 = 5^2 / 5^3 = 5^(2-3) = 5^-1 = 1/5^1 = 1/5\r<BR>\n" );
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document.write( "this has to do with properties of exponents.\r<BR>\n" );
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document.write( "the rule is:\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( "x^a is equal to 1 / x^(-a)\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "5^2 * 5^(-3) is equal to 5^2 * 1 / 5^3 which is equal to 5^2 / 5^3.\r<BR>\n" );
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document.write( "another rule is:\r<BR>\n" );
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document.write( "x^a / x^b = x^(a-b)\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "5^2 / 5^3 is equal to 5^(2-3) which is equal to 5^(-1) which is equal to 1/5.\r<BR>\n" );
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document.write( "here's some good references on exponent arithmetic.\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( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut29_negexp.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut23_exppart1.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut23_exppart1.htm</a>\r<BR>\n" );
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document.write( "in fact, this website has many tutorials that are hugely helpful as tutorials and as references.\r<BR>\n" );
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document.write( "here's the main website.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm</a>\r<BR>\n" );
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document.write( "on the questions of negative exponents, here's some more useful information.\r<BR>\n" );
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document.write( "if the negative exponents is in the numerator, then place it in the denominator and make the exponent positive.\r<BR>\n" );
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document.write( "if the negative expnent is in the denominator, then place it in the numerator and make the exponent positive.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "5^(-3) / 5^(-5) = 5^5 / 5^3 = 5^(5-3) = 25\r<BR>\n" );
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document.write( "this could also have been solved without doing that because:\r<BR>\n" );
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document.write( "5^(-3) / 5^(-5) = 5^(-3 - (-5)) = 5^(-3 + 5) = 5^2 = 25\r<BR>\n" );
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document.write( "note that numerator and denominator are always there but implied because:\r<BR>\n" );
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document.write( "any number by itself has a denominator of 1 and is also multiplied by 1.\r<BR>\n" );
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document.write( "therefore 5^(-3) = (1 * 5^(-3)) / 1.\r<BR>\n" );
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document.write( "place it in the denominator and make the exponent positive and you have 1 / (5^3 * 1) which simplifies to 1 / 5^3.\r<BR>\n" );
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document.write( "practice a few and you should have it in reasonably short period of time.\r<BR>\n" );
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document.write( "don't foget to study the references and to do the sample questions as well.\r<BR>\n" );
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document.write( "this allows you to solidify your learning.\r<BR>\n" );
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document.write( "here's 1 last example:\r<BR>\n" );
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document.write( "25x^-3 is equal to 25/x^3.\r<BR>\n" );
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document.write( "the 25 stays on top because it has a positive exponent which is 1, since any number raised to the power of 1 is that same number.\r<BR>\n" );
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document.write( "the x^-3 goes to the denominator and the exponent is made positive.\r<BR>\n" );
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document.write( "note that the rationale for moving it to the denominator is as follows:\r<BR>\n" );
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document.write( "25 * x^3 is equal to 25 * 1 / x^3 which is equal to (25 * 1) / x^3 which is equal to 25 / x^3\r<BR>\n" );
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document.write( "likewise x^-3 / y^-3 is equal to (1/x^3) / (1/y^3) which is equal to (1/x^3) * (y^3/1) which is equal to (1 * y^3) / (x^3 * 1) which is equal to y^3 / x^3.\r<BR>\n" );
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document.write( "send me an email if you have any further questions on this\r<BR>\n" );
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document.write( " </SPAN>\n" );
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