document.write( "Question 26470: Chapter covers: Properties of Integral Exponents
\n" ); document.write( "Problem: It says to simplify each exponential expression.\r
\n" ); document.write( "\n" ); document.write( " () top & bottom half all in one parethesis
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\n" ); document.write( " 9y^4 + (x^-1)^-2
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\n" ); document.write( " x^-2 (y^2) \n" ); document.write( "
Algebra.Com's Answer #14318 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
You either mean this:\r\n" );
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document.write( "9y4     (x-1)-2\r\n" );
document.write( "———— + —————————\r\n" );
document.write( "x-2       y2\r\n" );
document.write( "\r\n" );
document.write( "or this:\r\n" );
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document.write( "9y4 + (x-1)-2\r\n" );
document.write( "—————————————\r\n" );
document.write( "   x-2y2 \r\n" );
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document.write( "I'll do both:\r\n" );
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document.write( "In either case, you must learn the rule for getting \r\n" );
document.write( "rid of negative exponents.\r\n" );
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document.write( "If a numerator (respectively, denominator) either is \r\n" );
document.write( "or has a factor which is an exponential with a \r\n" );
document.write( "negative exponent, then move the base and exponent \r\n" );
document.write( "to the denominator (respectively, to the numerator)\r\n" );
document.write( "and change the sign of the exponent to positive.\r\n" );
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document.write( "If it's this way:\r\n" );
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document.write( "9y4     (x-1)-2\r\n" );
document.write( "———— + —————————\r\n" );
document.write( "x-2       y2\r\n" );
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document.write( "  \r\n" );
document.write( "In the first fraction, move the x-2 from the \r\n" );
document.write( "denominator to the numerator and change the sign of\r\n" );
document.write( "the -2 exponent to +2 and write x2 in the numerator, \r\n" );
document.write( "and put a 1 in the denominator:\r\n" );
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document.write( "9y4x2     (x-1)-2\r\n" );
document.write( "————— + —————————\r\n" );
document.write( "  1         y2\r\n" );
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document.write( "In the second fraction multiply the outer exponent \r\n" );
document.write( "-2 by the inner exponent -1, getting +2 so it ends\r\n" );
document.write( "up having a positive exponent, and there is no \r\n" );
document.write( "negative exponent to get rid of:\r\n" );
document.write( "\r\n" );
document.write( "In the first fraction, move the x-2 from the \r\n" );
document.write( "denominator to the numerator and change the sign of \r\n" );
document.write( "the -2 exponent to +2 and write x2 in the numerator, \r\n" );
document.write( "and put a 1 in the denominator:\r\n" );
document.write( "\r\n" );
document.write( "9y4x2    x2\r\n" );
document.write( "————— + ———\r\n" );
document.write( "  1      y2\r\n" );
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document.write( "Now the LCD is y2, so to make the first fraction \r\n" );
document.write( "have this LCD for its denominator, multiply top \r\n" );
document.write( "and bottom by y2\r\n" );
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document.write( "9y4x2·y2    x2\r\n" );
document.write( "———————— + ———\r\n" );
document.write( "  1·y2      y2 \r\n" );
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document.write( "Add the exponents of y in the numerator of the \r\n" );
document.write( "first fraction, and eliminate the \"1·\" in the bottom\r\n" );
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document.write( "9y6x2    x2\r\n" );
document.write( "————— + ———\r\n" );
document.write( "  y2     y2\r\n" );
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document.write( "Add the numerators and place over the common \r\n" );
document.write( "denominator\r\n" );
document.write( "\r\n" );
document.write( "9y6x2 + x2\r\n" );
document.write( "——————————\r\n" );
document.write( "     y2     \r\n" );
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document.write( "You may not do any canceling here.  You can, however, \r\n" );
document.write( "factor out an x2 from the numerator, if you like:\r\n" );
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document.write( "x2(9y6 + 1)\r\n" );
document.write( "——————————\r\n" );
document.write( "    y2\r\n" );
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document.write( "=====================================\r\n" );
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document.write( "If you meant this:\r\n" );
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document.write( "9y4 + (x-1)-2\r\n" );
document.write( "—————————————\r\n" );
document.write( "   x-2y2 \r\n" );
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document.write( "Then In the second term on top, multiply the outer\r\n" );
document.write( "exponent -2 by the inner exponent -1 getting +2 so \r\n" );
document.write( "it ends up having a positive exponent, and there is\r\n" );
document.write( "no negative exponent to get rid of:\r\n" );
document.write( "\r\n" );
document.write( "9y4 + x2\r\n" );
document.write( "————————\r\n" );
document.write( "  x-2y2\r\n" );
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document.write( "Now x-2 is a factor of the denominator, so move it \r\n" );
document.write( "from denominator to numerator by changing the sign \r\n" );
document.write( "of the -2 exponent and writing it in the top as x2.\r\n" );
document.write( "However it must be a FACTOR of the numerator, so the\r\n" );
document.write( "two terms in the numerator must by enclosed in \r\n" );
document.write( "parentheses:\r\n" );
document.write( "\r\n" );
document.write( "x2(9y4 + x2)\r\n" );
document.write( "————————————\r\n" );
document.write( "    y2\r\n" );
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document.write( "This is as far as you can go.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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