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One ordered pair \((a,b) \)satisfies the two equations \(ab^4 = 12\) and \(a^5b^5 = 7776\). What is the value of \(a\) in this ordered pair?

 

Please help I have no clue how to do this!!!

 Sep 8, 2018
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\(a b^4 = 12 \Rightarrow a^5 b^{20} = 248832 \\ b^{15}=\dfrac{a^5 b^{20}}{a^5 b^5} = \dfrac{248832}{7776} = 32 \\ b = 32^{1/15} = 2^{1/3} \\ a b^4 = 12 \\ a \left(2^{1/3}\right)^4 = 12 \\ a 2^{4/3} = 2^2(3) \\ a = 3\cdot 2^{2/3} \)

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 Sep 8, 2018

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