One ordered pair \((a,b)\) satisfies the two equations \(ab^4 = 384\) and \(a^2 b^5 = 4608\). What is the value of a in this ordered pair?
a·b4 = 384 and a2·b5 = 4608 ---> a2·b5 / a·b4 = 4608 / 384 ---> a·b = 12
I tried various whole number values for a and b; none worked.
Square roots won't work either.
I tried cube roots, giving one value the cube root of 2 and the other the cube root of 4.
Finally: a = 3·21/3 and b = 2·41/3