(29^1.85)/(29^1.85)+(28^1.85)

asked by guest
on Nov 24, 2024 at 12:35 am



You asked:

Evaluate the expression: 291.85291.85+281.85\frac{{29}^{1.85}}{{29}^{1.85}} + {28}^{1.85}

MathBot Answer:

291.85291.85+281.85=1+56⋅2710⋅71720≈476.60056073629779075706848780495919\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

291.85291.85+281.85=291+85100⋅1291+85100+281+85100=291+1720⋅1291+85100+281+85100=293720⋅1291+85100+281+85100=29⋅291720⋅1291+85100+281+85100=29⋅291720⋅1291+1720+281+85100=29⋅291720⋅1293720+281+85100=29⋅291720⋅129⋅291720+281+85100=1+281+85100=1+281+1720=1+283720=1+56⋅2710⋅71720\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}

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