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# System

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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, 2022

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Substitute the first equation into the second: $$384b = 4068$$, meaning $$b = 12$$

Now, plug this back into the first equation, and solving for a gives us $$a = \color{brown}\boxed{1 \over 54}$$

Jun 29, 2022