Question

Match the following items by evaluating the expression for x=-3.

x^-3 1/9,-3,-1/3,9,1

x^-1 -1/3,1,9,1/9,-3

x^0 -3,9,-1/3,1/9,1

x^1 1/9,-3,-1/3,1,9

x^2 -3,1,9,1/9,-1/3

Answer 1

-3^-3=1/(-3^3)=-1/27 maybe a typo, because you don't have this as an option
could have been -3^-2=1/(-3^2)=1/9

-3^-1=1/(-3^1)=-1/3

-3^0=1

-3^1=-3

-3^2=9

Answer 2

The values of given expression at x=-3 are
`x^(-3)= -(1)/(27)`,
`x^(-1)=-(1)/(3)`,
`x^(0)=1`,
`x^(1)=-3` and
`x^(2)=9`.

Explanation:

We need to find the value of each expression at x=-3.

The given expression is

`x^(-3)`

It can be written as

`x^(-3)=(1)/(x^3)`
`[\because x^(-n)=(1)/(x^n)]`

Substitute x=-3 in the above expression.

`x^(-3)=(1)/((-3)^3)\Rightarrow -(1)/(27)`

Similarly,

`x^(-1)=(1)/(x)\Rightarrow -(1)/(3)`

`x^(0)=1`
`[\because x^(0)=1]`

`x^(1)=(-3)^1=-3`

`x^(2)=(-3)^2=9`

Therefore the values of given expression at x=-3 are
`x^(-3)= -(1)/(27)`,
`x^(-1)=-(1)/(3)`,
`x^(0)=1`,
`x^(1)=-3` and
`x^(2)=9`.