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

#2**+5 **

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

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

#2**+5 **

Best Answer

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

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