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jmc

algebra junior

Problem

Evaluate

2 7^{- \frac{1}{3}} + 3 2^{- \frac{2}{5}}

. Express your answer as a common fraction.

Solution

We have

2 7^{- \frac{1}{3}} + 3 2^{- \frac{2}{5}} = \frac{1}{2 7 ^{\frac{1}{3}}} + \frac{1}{3 2 ^{\frac{2}{5}}} = \frac{1}{( 3 ^{3} ) ^{\frac{1}{3}}} + \frac{1}{( 2 ^{5} ) ^{\frac{2}{5}}} = \frac{1}{3 ^{1}} + \frac{1}{2 ^{2}} = \frac{1}{3} + \frac{1}{4} = \frac{7}{12} .

Final answer

\frac{7}{12}