document.write( "Question 736563: (y^2/3)^3/4 simplify \n" ); document.write( "

Algebra.Com's Answer #852640 by ikleyn(53354) $\"\"$ $\"About$

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document.write( "We are given this expression  (y^(2/3))^(3/4)  to simplify.\r\n" );
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document.write( "We can consider it as a formula to calculate a value, like a machinery, or as an algorithm, or as a function.\r\n" );
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document.write( "Then the domain of this function is the set of all real numbers, \r\n" );
document.write( "     including positive numbers, negative numbers and 0 (zero).\r\n" );
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document.write( "According to Algebra rules, we should multiply the indexes.\r\n" );
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document.write( "So, if 'y' is non-negative,  y >= 0,  then it is simplified to\r\n" );
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document.write( "    y^((2/3)*(3/4)) = y^(1/2) = .\r\n" );
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document.write( "But if 'y' is negative,  then this formula is like a lame horse, because\r\n" );
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document.write( "the left side expression is defined at negative real values of 'y', while the right \r\n" );
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document.write( "side,  ,  is not defined at negative values of 'y'.\r\n" );
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document.write( "So, if we want formula  y^((2/3)*(3/4) =   be valid for negative  'y',  too,\r\n" );
document.write( "we should modify it this way \r\n" );
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document.write( "    y^((2/3)*(3/4)) = .\r\n" );
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document.write( "Then both sides will be identical over the whole domain of all real numbers.\r\n" );
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