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# I'm so confused!!!

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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?

Sep 8, 2018

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