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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

#2
+8720
+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
+59
0

Jun 29, 2019
#2
+8720
+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