You want a Python program that produces and writes in an external file a power table for the Base numbers $($ N $)$ from $1$ to $5$ and for exponents from $1$ to $5$ as shown.

The program must use a function created for the program $($using def$)$ that receives two arguments $($the base number and the exponent$)$ and returns to the main program the value to be written in the table. It is the main program that sends Write the values of the table.

You have to use the for cycle $($no while$).$ Although a specific table is requested, the program must be generic.

$2.$ Series evaluation. The following equation provides an approximation for the value of e$*$:

$E^{**}=x,ol{x}^{\frac{x}{2}}1!+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+$dots

Develop a program in Python that compares each of the approximations that are calculated with the corresponding value calculated with the exp$()$ function of the math module for a given value of $x.$ You must continue adding terms until the difference between the approximation and the value of the library function is less than

$0\mathrm{.}0001.$ The output must include each of the approximations that are obtained. It must also be sent to write the number of terms that is taken until convergence is reached according to the previously established criterion

$($Minor difference $0\mathrm{.}0001).$

The program must send to write the output $($as it appears below$)$ in an external file. You have to use the factorial calculation program you developed for the previous task and define it as a function within the program $($Using def$)$; do not use the factorial library function of math$().$

You will run the program twice: for $x=1$ and $x=2.$