0.1/4 〖(37.4-38.6)〗^4+5.428(37.4)

asked by guest
on Mar 16, 2025 at 5:35 am



You asked:

Evaluate the expression: 0.14(37.4−38.6)4+5.428⋅37.4\frac{0.1}{4 {\left( 37.4 - 38.6 \right)}^{4}} + 5.428 \cdot 37.4

MathBot Answer:

0.14(37.4−38.6)4+5.428⋅37.4=13155647816480000=203.0192563271604938‾\frac{0.1}{4 {\left( 37.4 - 38.6 \right)}^{4}} + 5.428 \cdot 37.4 = \frac{1315564781}{6480000} = 203.0192563\overline{271604938}

0.14(37.4−38.6)4+5.428⋅37.4=1104(37.4−38.6)4+5.428⋅37.4=1104(1875−38.6)4+5.428⋅37.4=1104(1875−1935)4+5.428⋅37.4=1104(−65)4+5.428⋅37.4=1104⋅1296625+5.428⋅37.4=1105184625+5.428⋅37.4=12510368+5.428⋅37.4=12510368+1357250⋅37.4=12510368+1357250⋅1875=12510368+2537591250=13155647816480000\begin{aligned}\frac{0.1}{4 {\left( 37.4 - 38.6 \right)}^{4}} + 5.428 \cdot 37.4&=\frac{\frac{1}{10}}{4 {\left( 37.4 - 38.6 \right)}^{4}} + 5.428 \cdot 37.4\\&=\frac{\frac{1}{10}}{4 {\left( \frac{187}{5} - 38.6 \right)}^{4}} + 5.428 \cdot 37.4\\&=\frac{\frac{1}{10}}{4 {\left( \frac{187}{5} - \frac{193}{5} \right)}^{4}} + 5.428 \cdot 37.4\\&=\frac{\frac{1}{10}}{4 {\left( \frac{-6}{5} \right)}^{4}} + 5.428 \cdot 37.4\\&=\frac{\frac{1}{10}}{4 \cdot \frac{1296}{625}} + 5.428 \cdot 37.4\\&=\frac{\frac{1}{10}}{\frac{5184}{625}} + 5.428 \cdot 37.4\\&=\frac{125}{10368} + 5.428 \cdot 37.4\\&=\frac{125}{10368} + \frac{1357}{250} \cdot 37.4\\&=\frac{125}{10368} + \frac{1357}{250} \cdot \frac{187}{5}\\&=\frac{125}{10368} + \frac{253759}{1250}\\&=\frac{1315564781}{6480000}\end{aligned}

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