Gator Tee Shirtz has determined that its productivity is given by the equation $f(x, y)=36 x^{1 / 4} y^{3 / 4}$, when $x$ units of labor and $y$ units of capital are used. Compute the marginal productivity of capital when $a^{4}$ units of labor and $b^{4}$ units of capital are used where $a$ and $b$ have the following values: \[ a=3, \text { and } b=6 \text {. } \] Round your answer to two decimal places.

Step 1 ：The productivity function is given by $f(x, y)=36 x^{1 / 4} y^{3 / 4}$.

Step 2 ：The marginal productivity of capital is given by the partial derivative of the productivity function with respect to $y$, denoted as $f_y$.

Step 3 ：We have $f_y = 36 x^{1 / 4} * \frac{3}{4} y^{-1 / 4}$.

Step 4 ：Substitute $x = a^4$ and $y = b^4$ into the equation, we get $f_y = 36 a * \frac{3}{4} b^{-1}$.

Step 5 ：Given $a = 3$ and $b = 6$, substitute these values into the equation, we get $f_y = 36 * 3 * \frac{3}{4} * \frac{1}{6}$.

Step 6 ：Calculate the above expression, we get $f_y = 27$.

Step 7 ：So, the marginal productivity of capital when $a^{4}$ units of labor and $b^{4}$ units of capital are used is 27.