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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

 Jun 29, 2019
edited by BIGChungus  Jun 29, 2019

Best Answer 

 #2
avatar+8842 
+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.

 

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

 Jun 29, 2019
 #1
avatar+100 
+1

nvm I got the answer

 Jun 29, 2019
 #2
avatar+8842 
+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

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