PLEASE HELP MEEEEE

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PLEASE HELP MEEEEE

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

BIGChungus Jun 29, 2019

edited by BIGChungus Jun 29, 2019

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$a^5b^5\ =\ 7776\\~\\ (ab)^5\ =\ 7776\\~\\ ab\ =\ \sqrt[5]{7776}\\~\\ ab\ =\ 6\\~\\ b\ =\ \frac6a$

We can substitute this value in for b in the other given equation.

$ab^4\ =\ 12\\~\\ a(\frac6a)^4\ =\ 12\\~\\ \frac{6^4}{a^3}\ =\ \frac{12}{1}\\~\\ 12a^3\ =\ 6^4\\~\\ a^3\ =\ \frac{6^4}{12}\\~\\ a^3\ =\ 108\\~\\ a\ =\ \sqrt[3]{108}$ _

hectictar Jun 29, 2019

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hectictar · Answer 1 · 2019-06-29T09:15:35

$a^5b^5\ =\ 7776\\~\\ (ab)^5\ =\ 7776\\~\\ ab\ =\ \sqrt[5]{7776}\\~\\ ab\ =\ 6\\~\\ b\ =\ \frac6a$

We can substitute this value in for b in the other given equation.

$ab^4\ =\ 12\\~\\ a(\frac6a)^4\ =\ 12\\~\\ \frac{6^4}{a^3}\ =\ \frac{12}{1}\\~\\ 12a^3\ =\ 6^4\\~\\ a^3\ =\ \frac{6^4}{12}\\~\\ a^3\ =\ 108\\~\\ a\ =\ \sqrt[3]{108}$ _

BIGChungus · Answer 2 · 2019-06-29T09:04:35

nvm I got the answer

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