A spring of force constant k is cut into three equal pieces. If these three pieces are connected in parallel, the force constant of the combination will be

If a force F is applied to a spring of force constant k and the spring extends by an amount x, then
$F=k x$
The extension x produced in a spring is proportional to its length. 

Thus, if the spring is cut into three equal pieces, the same force F will produce an extension x/3 in a piece. If $k^{\text{'}}$ is the force constant of the piece, we have
$F=k^{\text{'}}x/3$
Therefore, $\frac{k^{\text{'}}}{3}=k or k^{\text{'}}=3k$. 

Thus, the force constant of each piece is 3k. When springs are connected in parallel, the force constant of the combination is equal to the sum of the individual force constants of the springs so connected. 

Therefore, the force constant of the combination $=3 k+3 k+3 k=9 k$.