document.write( "Question 176864: How would you simplify a^2b/a^5b^3? Thanks so much. \n" ); document.write( "
Algebra.Com's Answer #131946 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First method: breaking everything into prime factors:\r\n" );
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document.write( "Write \"a%5E2\" as \"a%2Aa\"\r\n" );
document.write( "Write \"a%5E5\" as \"a%2Aa%2Aa%2Aa%2Aa\"\r\n" );
document.write( "Write \"b%5E3\" as \"b%2Ab%2Ab\"\r\n" );
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document.write( "Then we have:\r\n" );
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document.write( "\"%28a%2Aa%2Ab%29%2F%28a%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%29\"\r\n" );
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document.write( "Put a \"1\" factor on the top and bottom:\r\n" );
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document.write( "Then we cancel the two \"a\"'s on top with two of\r\n" );
document.write( "the \"a\"'s on the bottom:\r\n" );
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document.write( "Then we cancel the \"b\" in the top into one of the\r\n" );
document.write( "\"b\"'s in the bottom:\r\n" );
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document.write( "So all that didn't cancel out is\r\n" );
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document.write( "\"1%2F%28a%2Aa%2Aa%2Ab%2Ab%29\"\r\n" );
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document.write( "Then write the \"a%2Aa%2Aa\" as \"a%5E3\" and \"b%2Ab\" as \"b%5E2\"\r\n" );
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document.write( "\"1%2F%28a%5E3b%5E2%29\"\r\n" );
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document.write( "That way will always work, but here is another method:\r\n" );
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document.write( "Second method:\r\n" );
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document.write( "Put a 1 coefficient on top and bottom.\r\n" );
document.write( "Also put a 1 exponent on the \"b\" on top:\r\n" );
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document.write( "Now subtract the exponents of \"a\"\r\n" );
document.write( "That is subtract them \"largest minus smaller\"\r\n" );
document.write( "and put the result where the larger exponent\r\n" );
document.write( "was, that is, either the numerator or\r\n" );
document.write( "denominator.\r\n" );
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document.write( "In this case the larger exponents are both in the\r\n" );
document.write( "bottom, \r\n" );
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document.write( "so we subtract exponents of \"a\",\r\n" );
document.write( "5-2 getting 3, so we put \"a%5E3\" on the\r\n" );
document.write( "bottome because the larger exponent 5 was\r\n" );
document.write( "on the bottom.   \r\n" );
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document.write( "we also subtract exponents of \"b\",\r\n" );
document.write( "3-1 getting 2, so we put \"b%5E2\" on the\r\n" );
document.write( "bottom because the larger exponent 3 was\r\n" );
document.write( "on the bottom.\r\n" );
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document.write( "So we have:\r\n" );
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document.write( "or\r\n" );
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document.write( "\"%281%29%2F%28a%5E3b%5E2%29\"  \r\n" );
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document.write( "Edwin
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