To find the value of [tex]n[/tex] that satisfies the equation, we follow the steps shown below:
[tex](\frac{1}{36} )^n=216\\[/tex]
[tex](\frac{1}{6^2} )^n=6^3\\=>(6^{-2})^n=6^3[/tex]
The last statement above is true because for indices, [tex]\frac{1}{x^n} =x^{-n}[/tex], also [tex](x^a)^b=x^{ab}[/tex] so,
[tex]6^{-2n}=6^3\\=>-2n=3\\=>n=-\frac{3}{2}.[/tex]
So [tex]n=-\frac{3}{2}[/tex] is the only value of [tex]n[/tex] that satisfied this equation. The second option is the correct answer.
