The third proportional of a and $\frac{b^4}{4a}$ is :

$\frac{b^8}{16a^2}$ $\frac{b^8}{8a^2}$ $\frac{b^8}{8a^3}$ $\frac{b^8}{16a^3}$

$\frac{b^8}{16a^3}$

Using the direct formula, Third proportional of A and B = \(\frac{B\; \times\;B}{A}\) Third proportion = $\frac{\frac{b^4}{4a} \; \times\; \frac{b^4}{4a}}{a}$                         =  $\frac{b^8}{16a^3}$