document.write( "Question 209048: Please help me solve this problem: (5thrt5x^2y)^9
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Algebra.Com's Answer #158413 by Edwin McCravy(20064)\"\" \"About 
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Please help me solve this problem: (5thrt5x^2y)^9
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You don't \"solve\" it.  You only solve equations and inequalities.\r\n" );
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document.write( "You can only simplify or rewrite expressions.  You didn't quote\r\n" );
document.write( "the instructions for how you are to simplify or rewrite the\r\n" );
document.write( "expression.  There are two sets of instructions your teacher\r\n" );
document.write( "or book could have been talking about.\r\n" );
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document.write( "First possible instructions:\r\n" );
document.write( "Rewrite using no radicals (roots), using\r\n" );
document.write( "only fractional exponents.  Then we would\r\n" );
document.write( "rprecede this way:\r\n" );
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document.write( "\"%28root%285%2Cx%5E2y%29%29%5E9\"\r\n" );
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document.write( "replace \"root%285%2Cx%5E2y%29\" by \"%28x%5E2y%29%5E%281%2F5%29\"\r\n" );
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document.write( "\"%28%28x%5E2y%29%5E%281%2F5%29%29%5E9\"\r\n" );
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document.write( "Remove the outermost parentheses by multiplying\r\n" );
document.write( "the exponents \"1%2F5\" and \"9\" to get\r\n" );
document.write( "exponent \"9%2F5\"\r\n" );
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document.write( "\"%28x%5E2y%29%5E%289%2F5%29\"\r\n" );
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document.write( "Now we remove the parentheses by writing \"y\"\r\n" );
document.write( "as \"y%5E1\"\r\n" );
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document.write( "\"%28x%5E2y%5E1%29%5E%289%2F5%29\"\r\n" );
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document.write( "And multiplying each inner exponent, \"2\" and \"1\"\r\n" );
document.write( "by the outer exponent \"9%2F5\", getting\r\n" );
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document.write( "-------------\r\n" );
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document.write( "However if the instructions are to rewrite in simplest radical form,\r\n" );
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document.write( "then you do it this way instead:\r\n" );
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document.write( "\"%28root%285%2Cx%5E2y%29%29%5E9\"\r\n" );
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document.write( "Bring the exponent 9 inside the radical:\r\n" );
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document.write( "\"%28root%285%2C%28x%5E2y%29%29%5E9%29\"\r\n" );
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document.write( "Give the \"y\" an eponent of \"1\"\r\n" );
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document.write( "\"%28root%285%2C%28x%5E2y%5E1%29%29%5E9%29\"\r\n" );
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document.write( "Remove the parentheses by multiplying inner exponents\r\n" );
document.write( "by the outer exponent.\r\n" );
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document.write( "\"root%285%2Cx%5E%282%2A9%29y%5E%281%2A9%29%29\"\r\n" );
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document.write( "\"root%285%2Cx%5E18y%5E9%29\"\r\n" );
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document.write( "Since both inside exponents are larger than the index\r\n" );
document.write( "5, we do this division by the index of the radical, 5:\r\n" );
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document.write( "   3         1\r\n" );
document.write( " ---         -\r\n" );
document.write( "5)18       5)9\r\n" );
document.write( "  15         5\r\n" );
document.write( "  --         -\r\n" );
document.write( "   3         4  \r\n" );
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document.write( "The quotients are the exponents of their bases IN FRONT\r\n" );
document.write( "OF the radical and the remainders are the powers UNDER\r\n" );
document.write( "the radical.\r\n" );
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document.write( "\"x%5E3y%5E1%2Aroot%285%2Cx%5E3y%5E4%29\"\r\n" );
document.write( "\"x%5E3y%2Aroot%285%2Cx%5E3y%5E4%29\"\r\n" );
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document.write( "Edwin
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