We have to find the missing parts of the table for the function:
![y=((1)/(7))^x](https://img.qammunity.org/2023/formulas/mathematics/college/pi3r115w893pljo3umnljo2vx3mq1wy4bu.png)
This will be done by replacing each x-value onto the function.
For x=-2
We obtain:
![y=((1)/(7))^(-2)=((7)/(1))^2=7^2=49](https://img.qammunity.org/2023/formulas/mathematics/college/mun93on9hbppc4lw62w698aie5wd4dmzsg.png)
This means that for x=-2, the value of y is 49.
For x=0
As every number (except 0) elevated to 0 is 1, we have
![y=((1)/(7))^0=1](https://img.qammunity.org/2023/formulas/mathematics/college/yhf2sjf1wqi8sk64khqtzgc93oauuy9zee.png)
This means that for x=0, the value of y is 1.
For x=2
![y=((1)/(7))^2=(1^2)/(7^2)=(1)/(49)](https://img.qammunity.org/2023/formulas/mathematics/college/qajnxmnwxvv1ud2zbmyfntviaa9w2szenh.png)
This means that for x=2, the value of y is 1/49.