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

To find the total time in hours, we need to add the given fractions of hours together. Given: - \( 2 / 3 \) hour - \( 2^{1 / 4} \) hours - \( 4^{1 / 3} \) hours Let's convert each fraction of hours to a decimal and then add them together to find the total time in hours. Calculate the value by following steps: - step0: Calculate: \(\frac{2}{3}+2^{\frac{1}{4}}+4^{\frac{1}{3}}\) - step1: Reduce fractions to a common denominator: \(\frac{2}{3}+\frac{2^{\frac{1}{4}}\times 3}{3}+\frac{4^{\frac{1}{3}}\times 3}{3}\) - step2: Transform the expression: \(\frac{2+2^{\frac{1}{4}}\times 3+4^{\frac{1}{3}}\times 3}{3}\) - step3: Reorder the terms: \(\frac{2+3\times 2^{\frac{1}{4}}+4^{\frac{1}{3}}\times 3}{3}\) - step4: Reorder the terms: \(\frac{2+3\times 2^{\frac{1}{4}}+3\times 4^{\frac{1}{3}}}{3}\) - step5: Simplify: \(\frac{2+3\sqrt[4]{2}+3\sqrt[3]{4}}{3}\) The total time in hours is approximately 3.443275 hours.