0.1/4 (39.87-38.6)^4+5.428(39.87)

asked by guest
on Mar 16, 2025 at 5:34 am



You asked:

Evaluate the expression: 0.14(39.87−38.6)4+5.428⋅39.87\frac{0.1}{4 {\left( 39.87 - 38.6 \right)}^{4}} + 5.428 \cdot 39.87

MathBot Answer:

0.14(39.87−38.6)4+5.428⋅39.87=14075383997361196503616025000≈216.42397003844011532030752076880185\frac{0.1}{4 {\left( 39.87 - 38.6 \right)}^{4}} + 5.428 \cdot 39.87 = \frac{1407538399736119}{6503616025000} \approx 216.42397003844011532030752076880185

0.14(39.87−38.6)4+5.428⋅39.87=1104(39.87−38.6)4+5.428⋅39.87=1104(3987100−38.6)4+5.428⋅39.87=1104(3987100−1935)4+5.428⋅39.87=1104(127100)4+5.428⋅39.87=1104⋅260144641100000000+5.428⋅39.87=11026014464125000000+5.428⋅39.87=2500000260144641+5.428⋅39.87=2500000260144641+1357250⋅39.87=2500000260144641+1357250⋅3987100=2500000260144641+541035925000=14075383997361196503616025000\begin{aligned}\frac{0.1}{4 {\left( 39.87 - 38.6 \right)}^{4}} + 5.428 \cdot 39.87&=\frac{\frac{1}{10}}{4 {\left( 39.87 - 38.6 \right)}^{4}} + 5.428 \cdot 39.87\\&=\frac{\frac{1}{10}}{4 {\left( \frac{3987}{100} - 38.6 \right)}^{4}} + 5.428 \cdot 39.87\\&=\frac{\frac{1}{10}}{4 {\left( \frac{3987}{100} - \frac{193}{5} \right)}^{4}} + 5.428 \cdot 39.87\\&=\frac{\frac{1}{10}}{4 {\left( \frac{127}{100} \right)}^{4}} + 5.428 \cdot 39.87\\&=\frac{\frac{1}{10}}{4 \cdot \frac{260144641}{100000000}} + 5.428 \cdot 39.87\\&=\frac{\frac{1}{10}}{\frac{260144641}{25000000}} + 5.428 \cdot 39.87\\&=\frac{2500000}{260144641} + 5.428 \cdot 39.87\\&=\frac{2500000}{260144641} + \frac{1357}{250} \cdot 39.87\\&=\frac{2500000}{260144641} + \frac{1357}{250} \cdot \frac{3987}{100}\\&=\frac{2500000}{260144641} + \frac{5410359}{25000}\\&=\frac{1407538399736119}{6503616025000}\end{aligned}

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