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

MathBot Answer:

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

\[\begin{aligned}\frac{38.095 \cdot \left(38.095 + 1\right) \cdot \left(2 + 38.095\right) \cdot \left(4 + 38.095\right)}{\left(3 + 38.095\right) \cdot \left(10 + 4 \cdot 38.095\right)}& = \left(38 + \frac{95}{1000}\right) \cdot \left(38 + \frac{95}{1000} + 1\right) \cdot \left(2 + 38 + \frac{95}{1000}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \left(38 + \frac{19}{200}\right) \cdot \left(38 + \frac{95}{1000} + 1\right) \cdot \left(2 + 38 + \frac{95}{1000}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \left(38 + \frac{95}{1000} + 1\right) \cdot \left(2 + 38 + \frac{95}{1000}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \left(38 + \frac{19}{200} + 1\right) \cdot \left(2 + 38 + \frac{95}{1000}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \left(\frac{7619}{200} + 1\right) \cdot \left(2 + 38 + \frac{95}{1000}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \left(2 + 38 + \frac{95}{1000}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \left(2 + 38 + \frac{19}{200}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \left(40 + \frac{19}{200}\right) \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \left(4 + 38 + \frac{95}{1000}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \left(4 + 38 + \frac{19}{200}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \left(42 + \frac{19}{200}\right) \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\left(3 + 38 + \frac{95}{1000}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\left(3 + 38 + \frac{19}{200}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\left(41 + \frac{19}{200}\right) \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\frac{8219}{200} \cdot \left(10 + 4 \cdot \left(38 + \frac{95}{1000}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\frac{8219}{200} \cdot \left(10 + 4 \cdot \left(38 + \frac{19}{200}\right)\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\frac{8219}{200} \cdot \left(10 + 4 \cdot \frac{7619}{200}\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\frac{8219}{200} \cdot \left(10 + \frac{7619}{50}\right)}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\frac{8219}{200} \cdot \frac{8119}{50}}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{8419}{200} \cdot \frac{1}{\frac{66730061}{10000}}\\& = \frac{7619}{200} \cdot \frac{7819}{200} \cdot \frac{8019}{200} \cdot \frac{420950}{66730061}\\& = \frac{59572961}{40000} \cdot \frac{8019}{200} \cdot \frac{420950}{66730061}\\& = \frac{477715574259}{8000000} \cdot \frac{420950}{66730061}\\& = \frac{4021887419686521}{10676809760000}\end{aligned}\]

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