Answer: The required match is
[tex]\left(x^{-2},\dfrac{1}{9}\right);~\left(x^{-1},-\dfrac{1}{3}\right);~(x^0,1);~(x^1,-3),~(x^2,9).[/tex]
Step-by-step explanation: We are given to match the following items with the given options by evaluating the expression for x = -3.
[tex]x^{-2},~~x^{-1},~~x^0,~~x^1,~~x^2.[/tex]
We will be using the following property of exponents :
[tex]a^{-b}=\dfrac{1}{a^b}.[/tex]
we have
[tex]x^{-2}=\dfrac{1}{x^2}=\dfrac{1}{(-3)^2}=\dfrac{1}{9},\\\\\\x^{-1}=\dfrac{1}{x}=\dfrac{1}{(-3)}=-\dfrac{1}{3},\\\\\\x^0=1,\\\\\\x^1=x=-3,\\\\\\x^2=(-3)^2=9.[/tex]
Thus, the required match is
[tex]\left(x^{-2},\dfrac{1}{9}\right);~\left(x^{-1},-\dfrac{1}{3}\right);~(x^0,1);~(x^1,-3),~(x^2,9).[/tex]
