Math Problem Solver

\[\frac{{29}^{1.85}}{{29}^{1.85}} + {28}^{1.85} = 1 + 56 \cdot 2^{\frac{7}{10}} \cdot 7^{\frac{17}{20}} \approx 476.60056073629779075706848780495919\]

\[\begin{aligned}\frac{{29}^{1.85}}{{29}^{1.85}} + {28}^{1.85}& = 29^{1 + \frac{85}{100}} \cdot \frac{1}{29^{1 + \frac{85}{100}}} + 28^{1 + \frac{85}{100}}\\& = 29^{1 + \frac{17}{20}} \cdot \frac{1}{29^{1 + \frac{85}{100}}} + 28^{1 + \frac{85}{100}}\\& = 29^{\frac{37}{20}} \cdot \frac{1}{29^{1 + \frac{85}{100}}} + 28^{1 + \frac{85}{100}}\\& = 29 \cdot 29^{\frac{17}{20}} \cdot \frac{1}{29^{1 + \frac{85}{100}}} + 28^{1 + \frac{85}{100}}\\& = 29 \cdot 29^{\frac{17}{20}} \cdot \frac{1}{29^{1 + \frac{17}{20}}} + 28^{1 + \frac{85}{100}}\\& = 29 \cdot 29^{\frac{17}{20}} \cdot \frac{1}{29^{\frac{37}{20}}} + 28^{1 + \frac{85}{100}}\\& = 29 \cdot 29^{\frac{17}{20}} \cdot \frac{1}{29 \cdot 29^{\frac{17}{20}}} + 28^{1 + \frac{85}{100}}\\& = 1 + 28^{1 + \frac{85}{100}}\\& = 1 + 28^{1 + \frac{17}{20}}\\& = 1 + 28^{\frac{37}{20}}\\& = 1 + 56 \cdot 2^{\frac{7}{10}} \cdot 7^{\frac{17}{20}}\end{aligned}\]