One ordered pair $ (a, b) $ satisfies the two equations $ab^4 = 12$ and $a^5 b^5 = 7776$. what is the value of $a$ in this ordered pair?

This is the concept of algebra, given that ab^4=12 and a^5b^5=7776, the value if a will be found as follows:

ab^4=12

a=12/b^4

also;

a^5=7776/b^5

thus;

a = (7776/b^5) ^ (1/5)

a=6/b

thus the value of a will be:

6/b=12/b^4

dividing both sides by b we get:

6=12/b^3

multiplying both sides by b^3 we get

6b^3=12

b^3=2

hence;

b=2^ (1/3)