The product of three numbers in continued proportion is $64$. Find the mean proportional.

If $\mathrm{x}, 2\mathrm{x}+1, 4\mathrm{x}+5$ are in continued proportion, then what is the value of $\mathrm{x}$?

What is the third proportional to $4 \& 18$?

What is the fourth proportional to $5, 10,\& 8$ ?

If the fourth proportional of  $\mathrm{ab}, \mathrm{bc} \& \mathrm{ca}$ is equal to ${\mathrm{c}}^k$, then find the value of $k$.

If $6, 9, 3\mathrm{x} + 2, 21$ are in proportion, find the value of $\mathrm{x}$ ?

If the third proportional to ${\mathrm{x}}^3\mathrm{y} \& {\mathrm{x}}^2{\mathrm{y}}^2$ is equal to $x{y}^k$, then find the value of $k$.

What is the fourth proportional to$\left({\mathrm{x}}^2-{\mathrm{y}}^2\right)\left({\mathrm{x}}^2\mathrm{y}-{\mathrm{xy}}^2\right) \& \left(\mathrm{x}+\mathrm{y}\right)$ ?