One ordered pair \((a, b)\) satisfies the two equations \(ab^4=384\) and \(a^2b^5=4608\). What is the value of \(a\) in this ordered pair?

iamhappy Jul 9, 2020

#1**0 **

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)**

I'm pretty surre I already answered this...

MathWizPro Jul 9, 2020