Algebra.Com's Answer #832963 by greenestamps(13200)![\"\"](\"/images/stars/stars-13.gif\")  You can put this solution on YOUR website! \n" ); document.write( "**************************************************************** \n" ); document.write( "Ignore this response; it is faulty. Some of the prime factors can be combined to give a smaller value of a+b+c than shown in my response. \n" ); document.write( "**************************************************************** \n" ); document.write( "Find the prime factorization of 648000. Since doing that doesn't give you practice in any particularly useful skills, I would use an online calculator. \n" ); document.write( "648000 = (2^6)(3^4)(5^3) \n" ); document.write( "So \n" ); document.write( "(a^2)(b^3)(c^4) = (2^6)(3^4)(5^3) \n" ); document.write( "Because that is a prime factorization, each exponent on the right must be a multiple of an exponent on the left. That means \n" ); document.write( "(1) 5^3 = b^3, so b is 5; and \n" ); document.write( "(2) 3^4 = c^4, so c is 4 \n" ); document.write( "That leaves a^2 = 2^6 = (2^3)^2, so a is 2^3 = 8 \n" ); document.write( "So for this particular problem there is only one value of a+b+c with a, b, and c distinct positive integers greater than 1. \n" ); document.write( "ANSWER: a+b+c = 8+5+4 = 17 \r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |