$\ln \left(\sqrt[4]{e^{3}}\right)$

Step 1 ：The problem is asking for the natural logarithm of the fourth root of e to the power of 3.

Step 2 ：The natural logarithm of a number is the exponent to which the base e must be raised to produce that number.

Step 3 ：The fourth root of a number is the number that would have to be multiplied by itself 4 times to get the original number.

Step 4 ：The exponent of e in the expression is 3.

Step 5 ：We can simplify the expression inside the logarithm first. The fourth root of e to the power of 3 is the same as e to the power of 3/4.

Step 6 ：Then, we can take the natural logarithm of e to the power of 3/4.

Step 7 ：The natural logarithm of e to the power of x is just x.

Step 8 ：So, the natural logarithm of e to the power of 3/4 is 3/4.

Step 9 ：Final Answer: \(\boxed{0.75}\)