Answer
$a.$
Conjecture:
(the cube root of a number) = ($\displaystyle \frac{1}{3}$ power of a number)
$b.$
Our conjecture works on $8$ and $27.$
Work Step by Step
$a.$
Generalizing on the pattern we observed in exercises 1-5:
(the square root of a number) = ($\displaystyle \frac{1}{2}$ power of a number),
We hypothesize that:
(the cube root of a number) = ($\displaystyle \frac{1}{3}$ power of a number)
$b.$
We know that $2^{3}=8$, so $\sqrt[3]{8}=2$
The calculator returns $8^{\wedge}(1\div 3)=2$ as well.
We know that $3^{3}=27$, so $\sqrt[3]{27}=3$
The calculator returns $27^{\wedge}(1\div 3)=3$ as well
So, our conjecture works for $8$ and $27.$
