Answer:
The value of b = 1/36
As exponent decreases, each previous value is divided by 6
If the table was extended, the value of 6^-3 would be 1/216
Explanation:
Given in the question a table containing power of 6
We will use negative rule of exponent to write the equivalent of negative power of 6
b^{-n}= 1 / b^{n}
we know that
![6^(1)=6](https://img.qammunity.org/2020/formulas/mathematics/middle-school/wf8akbz74m74dzob7d4e0m65gnu4ke7czo.png)
so
= 1/6
and
![6^(2) = 36](https://img.qammunity.org/2020/formulas/mathematics/middle-school/pzpu3khsfircopgomzcv6yg1n11p18myub.png)
So,
![6^(-2) = (1)/(6^(2) )](https://img.qammunity.org/2020/formulas/mathematics/middle-school/3kp3faoeiw67ok4t0y4oukmedqp15dr2gn.png)
=
![(1)/(36)](https://img.qammunity.org/2020/formulas/physics/high-school/e5c8fv8guljfioh4iy26qidycoipaokp.png)