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# Algebra help

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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