document.write( "Question 62417: Hi,
\n" ); document.write( "Can you please show me the steps needed to solve this?\r
\n" ); document.write( "\n" ); document.write( "((3^-2)^a).((3^b)^-2a)
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\n" ); document.write( "((3^-2)^b).((9^-b)^3a)\r
\n" ); document.write( "\n" ); document.write( "three to the negative two to the a times three to the b to the negative two a
\n" ); document.write( "divided by
\n" ); document.write( "three to the negative two to the b times nine to the negative b to the three a\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance!!\r
\n" ); document.write( "\n" ); document.write( "Ray \n" ); document.write( "
Algebra.Com's Answer #43172 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Hi,\r\n" );
document.write( "Can you please show me the steps needed to solve this?\r\n" );
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document.write( "((3^-2)^a).((3^b)^(-2a))\r\n" );
document.write( "----------------------\r\n" );
document.write( "((3^-2)^b).((9^-b)^(3a))\r\n" );
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document.write( "three to the negative two to the a times three to the\r\n" );
document.write( "b to the negative two a divided by\r\n" );
document.write( "three to the negative two to the b times nine to the \r\n" );
document.write( "negative b to the three a\r\n" );
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document.write( "Thanks in advance!!\r\n" );
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document.write( "Ray\r\n" );
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document.write( " (3-2)a(3b)-2a\r\n" );
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document.write( " (3-2)b(9-b)3a\r\n" );
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document.write( "First multiply the outer exponents by the inner \r\n" );
document.write( "exponents to remove the parentheses:\r\n" );
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document.write( " 3-2a3-2ab\r\n" );
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document.write( " 3-2b9-3ab\r\n" );
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document.write( "Rewrite the 9 as (32)\r\n" );
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document.write( "   3-2a3-2ab\r\n" );
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document.write( " 3-2b(32)-3ab\r\n" );
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document.write( "Remove the parentheses by multiplying the outer \r\n" );
document.write( "exponent -3ab by the inner exponent 2, getting\r\n" );
document.write( "-6ab:\r\n" );
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document.write( " 3-2a3-2ab\r\n" );
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document.write( " 3-2b3-6ab\r\n" );
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document.write( "Get rid of each negative exponent by using the \r\n" );
document.write( "rules:\r\n" );
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document.write( "1. To get rid of a negative exponent in the \r\n" );
document.write( "   numerator, move the base and exponent from \r\n" );
document.write( "   the numerator to the denominator and\r\n" );
document.write( "   change the sign of the exponent to positive.\r\n" );
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document.write( "2. To get rid of a negative exponent in the \r\n" );
document.write( "   denominator, move the base and exponent from \r\n" );
document.write( "   the denominator to the numerator and\r\n" );
document.write( "   change the sign of the exponent to positive.\r\n" );
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document.write( "So move the 3-2a from the top to the bottom as 32a,\r\n" );
document.write( "move the 3-2ab from the top to the bottom as 32ab,\r\n" );
document.write( "move the 3-2b from the bottom to the top as 32b, and\r\n" );
document.write( "move the 3-6ab from the bottom to the top as 36ab\r\n" );
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document.write( " 32b36ab\r\n" );
document.write( "---------\r\n" );
document.write( " 32a32ab\r\n" );
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document.write( "Now on the top we add the exponents of 3, which \r\n" );
document.write( "are 2b and 6ab, getting 2b+6ab \r\n" );
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document.write( "On the bottom we also add the exponents of 3, \r\n" );
document.write( "which are 2a and 2ab, getting 2a+2ab\r\n" );
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document.write( " 32b+6ab\r\n" );
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document.write( " 32a+2ab\r\n" );
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document.write( "Finally we subtract exponents (2b+6ab)-(2a+2ab)\r\n" );
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document.write( "3(2a+6ab)-(2a+2ab)\r\n" );
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document.write( "32b+6ab-2a-2ab\r\n" );
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document.write( "32b-2a+4ab\r\n" );
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document.write( "or if you like, factor out\r\n" );
document.write( "2 in the exponent:\r\n" );
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document.write( "32(b-a+2ab)\r\n" );
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document.write( "Edwin
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