document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107137>Question 107137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I simplify (3a^2b^3)^4. Someone please help me I have a test coming up soon.<BR>\n" );
document.write( "Thank You,<BR>\n" );
document.write( "Ty </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77959 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=77959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To do this problem, you need to raise each of the individual terms inside the parentheses<BR>\n" );
document.write( "to the 4th power. <BR>\n" );
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document.write( "In other words:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Aa%5E2%2Ab%5E3%29%5E4 ALIGN=MIDDLE  ALT=\"%283%2Aa%5E2%2Ab%5E3%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%5E4%29%2A%28a%5E2%29%5E4%2A%28b%5E3%29%5E4%29 ALIGN=MIDDLE  ALT=\"%28%283%5E4%29%2A%28a%5E2%29%5E4%2A%28b%5E3%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can recognize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 3*3*3*3 and this product is 81. So you can substitute<BR>\n" );
document.write( "81 in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4 ALIGN=MIDDLE  ALT=\"3%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the problem is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2A%28a%5E2%29%5E4%2A+%28b%5E3%29%5E4 ALIGN=MIDDLE  ALT=\"81%2A%28a%5E2%29%5E4%2A+%28b%5E3%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%29%5E4 ALIGN=MIDDLE  ALT=\"%28a%5E2%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You can get an equivalent form of this by multiplying the exponent<BR>\n" );
document.write( "4 by the exponent 2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E8 ALIGN=MIDDLE  ALT=\"a%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You can also think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%29%5E4 ALIGN=MIDDLE  ALT=\"%28a%5E2%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiplied by itself 4 times and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2+=+a%5E8 ALIGN=MIDDLE  ALT=\"a%5E2%2Aa%5E2%2Aa%5E2%2Aa%5E2+=+a%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute this into the<BR>\n" );
document.write( "problem and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2Aa%5E8%2A%28b%5E3%29%5E4 ALIGN=MIDDLE  ALT=\"81%2Aa%5E8%2A%28b%5E3%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, you can raise <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E3%29 ALIGN=MIDDLE  ALT=\"%28b%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the 4th power by multiplying the exponent 4 times<BR>\n" );
document.write( "the exponent 3 to get an exponent 12. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E3%29%5E4+=+b%5E12 ALIGN=MIDDLE  ALT=\"%28b%5E3%29%5E4+=+b%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Think:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E3%2Ab%5E3%2Ab%5E3%2Ab%5E3+=+b%5E12 ALIGN=MIDDLE  ALT=\"b%5E3%2Ab%5E3%2Ab%5E3%2Ab%5E3+=+b%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Substitute this and you get the answer to the problem as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2Aa%5E8%2Ab%5E12 ALIGN=MIDDLE  ALT=\"81%2Aa%5E8%2Ab%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to solve it.  Good luck on the test ...<BR>\n" );
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