SOLUTION: If {{{ (1/125)^(a^2+4ab) = ( 625^(1/3) )^(3a^2-10ab) }}} and if a and b do not equal 0, find {{{ a/b }}} .

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If {{{ (1/125)^(a^2+4ab) = ( 625^(1/3) )^(3a^2-10ab) }}} and if a and b do not equal 0, find {{{ a/b }}} .      Log On


   

Question 1060615: If +%281%2F125%29%5E%28a%5E2%2B4ab%29+=+%28+625%5E%281%2F3%29+%29%5E%283a%5E2-10ab%29+ and if a and b do not equal 0, find +a%2Fb+ .
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1/125^(aČ+4ab)=(625^(1/3))^(3aČ-10ab)
(5^-3)^(aČ+4ab)=((5^4)^(1/3))^(3aČ-10ab)
5^(-3aČ-12ab)=5^4aČ-40ab/3
-3aČ-12ab=4aČ-(40ab/3)
-9aČ-36ab=12aČ-40ab
4ab=21aČ
4b=21a
21a/b=4
a/b=4/21. ☺☺☺☺