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

 Jun 29, 2021
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ab^5 is basically ab^4 * b. Plugging in known values and simplifying,

\(ab^5 = ab^4 \cdot b\)

\(4608 = 384\cdot b\)

\(b = 12\)

Plug b into one of the known equations,

\(a \cdot 12^4 = 384\)

\(a \cdot 20736 = 384\)

\(a = 1/54\)

So the value of a is 1/54.

 Jun 29, 2021

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