((38.095)*(38.095+1)*(2+38.095)*(4+38.095))/((3+38.095)*(10+4*38.095))

asked by guest
on Nov 20, 2024 at 8:31 am



You asked:

Evaluate the expression: 38.095(38.095+1)(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)\frac{38.095 \left(38.095 + 1\right) \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}

MathBot Answer:

38.095(38.095+1)(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)=402188741968652110676809760000≈376.69374186606477476470462090541173\frac{38.095 \left(38.095 + 1\right) \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)} = \frac{4021887419686521}{10676809760000} \approx 376.69374186606477476470462090541173

38.095(38.095+1)(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)=7619200(38.095+1)(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)=7619200(7619200+1)(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)=7619200⋅7819200(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)=5957296140000(2+38.095)(4+38.095)(3+38.095)(10+4⋅38.095)=5957296140000(2+7619200)(4+38.095)(3+38.095)(10+4⋅38.095)=5957296140000⋅8019200(4+38.095)(3+38.095)(10+4⋅38.095)=4777155742598000000(4+38.095)(3+38.095)(10+4⋅38.095)=4777155742598000000(4+7619200)(3+38.095)(10+4⋅38.095)=4777155742598000000⋅8419200(3+38.095)(10+4⋅38.095)=40218874196865211600000000(3+38.095)(10+4⋅38.095)=40218874196865211600000000(3+7619200)(10+4⋅38.095)=402188741968652116000000008219200(10+4⋅38.095)=402188741968652116000000008219200(10+4⋅7619200)=402188741968652116000000008219200(10+761950)=402188741968652116000000008219200⋅811950=402188741968652116000000006673006110000=402188741968652110676809760000\begin{aligned}\frac{38.095 \left(38.095 + 1\right) \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}&=\frac{\frac{7619}{200} \left(38.095 + 1\right) \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{7619}{200} \left(\frac{7619}{200} + 1\right) \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{7619}{200} \cdot \frac{7819}{200} \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{59572961}{40000} \left(2 + 38.095\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{59572961}{40000} \left(2 + \frac{7619}{200}\right) \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{59572961}{40000} \cdot \frac{8019}{200} \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{477715574259}{8000000} \left(4 + 38.095\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{477715574259}{8000000} \left(4 + \frac{7619}{200}\right)}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{477715574259}{8000000} \cdot \frac{8419}{200}}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{4021887419686521}{1600000000}}{\left(3 + 38.095\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{4021887419686521}{1600000000}}{\left(3 + \frac{7619}{200}\right) \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{4021887419686521}{1600000000}}{\frac{8219}{200} \left(10 + 4 \cdot 38.095\right)}\\&=\frac{\frac{4021887419686521}{1600000000}}{\frac{8219}{200} \left(10 + 4 \cdot \frac{7619}{200}\right)}\\&=\frac{\frac{4021887419686521}{1600000000}}{\frac{8219}{200} \left(10 + \frac{7619}{50}\right)}\\&=\frac{\frac{4021887419686521}{1600000000}}{\frac{8219}{200} \cdot \frac{8119}{50}}\\&=\frac{\frac{4021887419686521}{1600000000}}{\frac{66730061}{10000}}\\&=\frac{4021887419686521}{10676809760000}\end{aligned}

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