7. \( 2 / 3 \) hour \( +2^{1 / 4} \) hours \( +4^{1 / 3} \) hours

First, let's convert each time component into the same unit, which we can choose to be hours. The first component is \( \frac{2}{3} \) hours, which is straightforward. Next, we convert \( 2^{1/4} \) and \( 4^{1/3} \) into decimal form for easier addition: 1. \( 2^{1/4} \) is the fourth root of 2, which is approximately \( 1.189 \) hours. 2. \( 4^{1/3} \) is the cube root of 4, which is approximately \( 1.587 \) hours. Now, let's perform the addition: \[ \frac{2}{3} \approx 0.667 \text{ hours} \] So we can now add: \[ 0.667 + 1.189 + 1.587 \approx 3.443 \text{ hours} \] Hence, \( \frac{2}{3} \) hour \( + 2^{1/4} \) hours \( + 4^{1/3} \) hours is approximately \( 3.443 \) hours.