document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098110>Question 1098110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Commutative Property of Multiplication and the Associative Property of Multiplication to show the Power of a Product Property (a * b)^n = a^n * b^n is true. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837087 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The expression (a * b)^n means we have n copies of (a*b) multiplied together, where n is a positive integer.\r<BR>\n" );
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document.write( "Let's say for example we have (a*b)^3<BR>\n" );
document.write( "That leads to 3 copies of (a*b) multiplied<BR>\n" );
document.write( "(a*b)^3 = (a*b)*(a*b)*(a*b)\r<BR>\n" );
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document.write( "Then use the commutative property of multiplication<BR>\n" );
document.write( "a*b = b*a\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "(a*b)*(<font color=red>a*b</font>)*(a*b)<BR>\n" );
document.write( "is the same as<BR>\n" );
document.write( "(a*b)*(<font color=red>b*a</font>)*(a*b)\r<BR>\n" );
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document.write( "Then we use the associative property of multiplication<BR>\n" );
document.write( "(a*b)*(b*a)*(a*b)<BR>\n" );
document.write( "becomes<BR>\n" );
document.write( "a*(b*b)*a*(a*b)\r<BR>\n" );
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document.write( "Use the associative and commutative properties to rearrange terms so that we end up with <BR>\n" );
document.write( "(a*a*a)*(b*b*b)<BR>\n" );
document.write( "that condenses down into<BR>\n" );
document.write( "a^3*b^3\r<BR>\n" );
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document.write( "This example shows that (a*b)^3 = a^3*b^3\r<BR>\n" );
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document.write( "This can be extended more generally to (a*b)^n = a^n*b^n<BR>\n" );
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