Question

3^x^2(9^x)=1/3

Answer 1

http://www.wolframalpha.com/input/?i=3%5Ex%5E2%289%5Ex%29%3D1%2F3%2C+solve+for+x

x=-1

Answer 2

I don't get it

Answer 3

\[3^{x^2}(9^x)=1/3\]If that's the case, \[3^{x^2}(9^x)=1/3\]\[3^{x^2}(3^2)^x=1/3\]\[3^{x^2}(3^{2x})=1/3\]\[3^{x^2+2x}=1/3\]\[3^{x^2+2x}=3^{-1}\]Since the base is the same, you can equate the power.
So,
\[x^2 + 2x = -1\]Now, solve the equation.