The third proportional of a and (b^4)/4a is :

Using the direct formula,

Third proportional of A and B = \(\frac{B\; \times\;B}{A}\)

Third proportion = $\frac{\frac{b^4}{4a} \; \times\; \frac{b^4}{4a}}{a}$

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