Question 475131
<font face="Times New Roman" size="+2">


Break everything in the LHS into pieces:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(9a^2b\right)^x\,\cdot\,\left(3ab\right)^4\ =\ 9^x\,\cdot\,a^{2x}\,\cdot\,b^x\,\cdot\,3^4\,\cdot\,a^4\,\cdot\,b^4]


First thing to note is that *[tex \Large 3^4\ =\ 3^2\,\cdot\,3^2\ =\ 9\,\cdot\,9\ =\ 9^2]


Next, substitute and rearrange:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9^x\,\cdot\,9^2\,\cdot\,a^{2x}\,\cdot\,a^4\,\cdot\,b^x\,\cdot\,b^4] 


Use the sum of exponents rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9^{x\,+\,2}\,\cdot\,a^{2x\,+\,4}\,\cdot\,b^{x\,+\,4}]


Now this uglier-than-a-mud-fence expression is equivalent to the original Left Hand Side, which we were told was equal to the original right hand side, hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9^{x\,+\,2}\,\cdot\,a^{2x\,+\,4}\,\cdot\,b^{x\,+\,4}\ =\ 9^5\,\cdot\,a^{10}\,\cdot\,b^7]


Now all we need to do is find a value for *[tex \Large x] such that *[tex \Large x\ +\ 2\ =\ 5], and *[tex \Large 2x\ +\ 4\ =\ 10], and *[tex \Large x\ +\ 4\ =\ 7]


Can you take it from here?


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>