7. $$ 2 / 3 $$ hour $$ +2^{1 / 4} $$ hours $$ +4^{1 / 3} $$ hours

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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:
  $$\frac{2}{3}+\frac{2^{\frac{1}{4}}	imes 3}{3}+\frac{4^{\frac{1}{3}}	imes 3}{3}$$
- step2: Transform the expression:
  $$\frac{2+2^{\frac{1}{4}}	imes 3+4^{\frac{1}{3}}	imes 3}{3}$$
- step3: Reorder the terms:
  $$\frac{2+3	imes 2^{\frac{1}{4}}+4^{\frac{1}{3}}	imes 3}{3}$$
- step4: Reorder the terms:
  $$\frac{2+3	imes 2^{\frac{1}{4}}+3	imes 4^{\frac{1}{3}}}{3}$$
- step5: Simplify:
  $$\frac{2+3\sqrt[4]{2}+3\sqrt[3]{4}}{3}$$
The total time in hours is approximately 3.443275 hours.
The total time is approximately 3.44 hours.

hour hours hours

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