document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817811>Question 817811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (2x^-2)/(3y^3) ^-3<BR>\n" );
document.write( " simplify leaving positive exponents only  using rules of exponents </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492204 by </B><A HREF=/tutors/aboutme.mpl?userid=FightinBlueHens><B>FightinBlueHens(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FightinBlueHens><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=492204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (2x^-2)/(3y^3) ^-3<BR>\n" );
document.write( "Remember: When you raise a number to a negative power, first you have to make that number into its reciprocal, and then you raise it to that power.<BR>\n" );
document.write( "When you raise a power to a power (ex. (a^m)^n) you multpily the the powers that you are raising the number to because you are multiplying that power by itself a certain number of times. For example:<BR>\n" );
document.write( "(x^3)^2 = xxx*xxx = x*x*x*x*x*x which equals x^6\r<BR>\n" );
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document.write( "Just to be clear, the way it's written: <BR>\n" );
document.write( "1. in 2x^&#8722;2, you are raising x to the power of -2 and not the whole expression 2x to the -2<BR>\n" );
document.write( "2. you are raising y to the power of 3, and not 3y to the power of 3<BR>\n" );
document.write( "3. you are raising 3y^3 to the power of -3\r<BR>\n" );
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document.write( "First solve for the numerator: (2x^-2) = (2/x^2)<BR>\n" );
document.write( "The the denominator: For this the expression inside the parentheses is already in simplest form, so you just need to raise 3y^3 to the power of -3.<BR>\n" );
document.write( "This will become (1/3y^3)^3 (Now we don't have to deal with a negative value anymore.)<BR>\n" );
document.write( "1^3 = 1, 3^3 = 3*3*3 = 9*3 = 27<BR>\n" );
document.write( "(y^3)^3 = y^9<BR>\n" );
document.write( "(1/3y^3)^3 = 1/(27y^9).\r<BR>\n" );
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document.write( "(2/x^2)/ 1/(27y^9)<BR>\n" );
document.write( "When you divide by a fraction, you are multiplying by its reciprocal (you flip the fraction and then multiply by it), so when you divide by 1/(27y^9), you are multiplying by (27y^9)/1 whch equals 27y^9.\r<BR>\n" );
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document.write( "Multiply the numerators: 2*27y^9 = 54y^9<BR>\n" );
document.write( "Multiply the denominators: x^2*1 = x^2\r<BR>\n" );
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document.write( "Answer: 54y^9/x^2 </SPAN>\n" );
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