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?

Guest Jul 9, 2020

#1**+1 **

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Melody Jul 9, 2020

#2**0 **

\(ab^4 = 384\\ a^2 b^5 = 4608 \)

Considering the second equation:

\(ab^4 \cdot ab = 4608\\ ab = \dfrac{4608}{384} = 12\)

Considering the first equation:

\(ab^4 = 384\\ ab\cdot b^3 = 384\\ b = \sqrt[3]{\dfrac{384}{12}} = 2\sqrt[3]4\)

Substituting directly gives \(a =3 \sqrt[3]{2}\)

MaxWong Jul 9, 2020