document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463067>Question 463067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What do Laws of Exponent means?<BR>\n" );
document.write( "Explain and give some examples.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317330 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=317330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> these are the laws that i know of.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 1\r<BR>\n" );
document.write( "\n" );
document.write( "x^0 = 1\r<BR>\n" );
document.write( "\n" );
document.write( "this means that any number raised to the power of 0 is equal to 1.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 2\r<BR>\n" );
document.write( "\n" );
document.write( "x^1 = x\r<BR>\n" );
document.write( "\n" );
document.write( "this means that any number raised to the power of 1 is equal to the number.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 3\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 = x*x (x is multiplied by x 1 time)<BR>\n" );
document.write( "x^3 = x*x*x (x is multiplied by x 2 times)<BR>\n" );
document.write( "x^4 = x*x*x*x (x is multiplied by x 3 times)\r<BR>\n" );
document.write( "\n" );
document.write( "in general x^n means that x is multiplied by x (n-1) times.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 4\r<BR>\n" );
document.write( "\n" );
document.write( "a^b * a^c = a^(b+c)\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "2^2 + 2^3 = 2^(2+3) = 2^5 = 32.\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "2^2 = 4 and 2^3 = 8 and 4*8 = 32.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 5\r<BR>\n" );
document.write( "\n" );
document.write( "a^b / a^c = a^(b-c)\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "2^3 / 2^2 = 2^(3-2) = 2^1 = 2\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "2^3 = 8 and 2^2 = 4 and 8/4 = 2\r<BR>\n" );
document.write( "\n" );
document.write( "law number 6\r<BR>\n" );
document.write( "\n" );
document.write( "(a^b)^c = a^(b*c)\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "(2^2)^3 = 2^6 = 64\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "2^2 = 4 and 4^3 = 64\r<BR>\n" );
document.write( "\n" );
document.write( "law number 7\r<BR>\n" );
document.write( "\n" );
document.write( "a^(-b) = 1/(a^b)\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "2^(-3) = 1/(2^3) = 1/8\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "use your calculator to derive 2^(-3) and you will get an answer of .125\r<BR>\n" );
document.write( "\n" );
document.write( "use your calculator to derive 1/(2^3) and you will also get an answer of .125.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 8\r<BR>\n" );
document.write( "\n" );
document.write( "a^(1/b) = the bth root of a\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "64^(1/6) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C64%29 ALIGN=MIDDLE  ALT=\"root%286%2C64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "use your calculator to derive 64^(1/6) and you will get an answer of 2.\r<BR>\n" );
document.write( "\n" );
document.write( "use your calculator to derive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C64%29 ALIGN=MIDDLE  ALT=\"root%286%2C64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you will also get an answer of 2.\r<BR>\n" );
document.write( "\n" );
document.write( "law number 9\r<BR>\n" );
document.write( "\n" );
document.write( "(a*b)^c = a^b * a^c\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "(2*5)^3 = 2^3 * 5^3 = 8 * 125 = 1000\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "2*5 = 10 and 10^3 = 1000\r<BR>\n" );
document.write( "\n" );
document.write( "law number 10\r<BR>\n" );
document.write( "\n" );
document.write( "(a/b)^c = a^c / b^c\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "(10/5)^3 = 10^3 / 5^3 = 1000 / 125 = 8\r<BR>\n" );
document.write( "\n" );
document.write( "proof:\r<BR>\n" );
document.write( "\n" );
document.write( "(10/5)^3 = 2^3 = 8\r<BR>\n" );
document.write( "\n" );
document.write( "these are all i can remember off the top of my head.\r<BR>\n" );
document.write( "\n" );
document.write( "they should cover all or most of the exponent laws you will encounter.\r<BR>\n" );
document.write( "\n" );
document.write( "search the web for tutorials on \"laws of exponents\" and you will discover a wealth of material that you can reference.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );