Raise both sides of the first equation to the exponent y
[tex]a = 6^x\\\\a^y = (6^x)^y\\\\a^y = 6^{xy}\\\\[/tex]
Raise both sides of the second equation to the exponent of x.
[tex]b = 6^y\\\\b^x = (6^y)^x\\\\b^x = 6^{xy}\\\\[/tex]
Multiplying them gets us
[tex]a^y*b^x = 36\\\\6^{xy}*6^{xy} = 6^2\\\\6^{xy+xy} = 6^2\\\\6^{2xy} = 6^2\\\\2xy = 2\\\\xy = 2/2\\\\xy = 1\\\\[/tex]
This concludes the proof.
