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

Answer:

The values of given expression at x=-3 are $x^{-3}= -\frac{1}{27}$, $x^{-1}=-\frac{1}{3}$, $x^{0}=1$, $x^{1}=-3$ and $x^{2}=9$.

Step-by-step explanation:

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

The given expression is

$x^{-3}$

It can be written as

$x^{-3}=\frac{1}{x^3}$                     $[\because x^{-n}=\frac{1}{x^n}]$

Substitute x=-3 in the above expression.

$x^{-3}=\frac{1}{(-3)^3}\Rightarrow -\frac{1}{27}$

Similarly,

$x^{-1}=\frac{1}{x}\Rightarrow -\frac{1}{3}$

$x^{0}=1$                   $[\because x^{0}=1]$

$x^{1}=(-3)^1=-3$

$x^{2}=(-3)^2=9$

Therefore the values of given expression at x=-3 are $x^{-3}= -\frac{1}{27}$, $x^{-1}=-\frac{1}{3}$, $x^{0}=1$, $x^{1}=-3$ and $x^{2}=9$.