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?
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+9519 \(ab^4 = 384\\ a^2 b^5 = 4608 \)
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 \(a =3 \sqrt[3]{2}\)
