The expression given is:
[tex](3^3\cdot3^{-1})^{-2}[/tex]One property of exponents that we know is:
[tex]a^xa^y=a^{x+y}[/tex]We use this property shown above to simplify the expression:
[tex]\begin{gathered} (3^3\cdot3^{-1})^{-2} \\ =(3^{3-1})^{-2} \\ =(3^2)^{-2} \end{gathered}[/tex]Now, we use the power property of exponents, which is:
[tex](a^b)^c=a^{bc}[/tex]to simplify our expression, fully:
[tex]\begin{gathered} (3^2)^{-2} \\ =3^{2\times-2} \\ =3^{-4} \end{gathered}[/tex]Using the property:
[tex]a^{-n}=\frac{1}{a^n}[/tex]we can write the answer as:
[tex]3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]From the choices, given, we can say:
• 2nd choice is correct
,• 3rd choice is correct
[tex]3^{-11}\cdot3^7=3^{-11+7}=3^{-4}[/tex]