Design and implement $($meaning write code and execute the code turning in test cases and source code$)$ for the following two algorithms to raise an integer to an integer power assume in both cases that n$,$ the exponent, is a power of $2$:

Again, in case you don$$t have any programming language at hand you can use pseudocode to solve the problem.

Algorithm $1$

X$**$N $=$ X$*$ X$**($N$-1)$

X$**0=1$

Algorithm $2$

n $=2**$m

X$**$n $=(($X$**2)**2)**2...,$ etc. $[$NOTE: the symbol of power $(**)$ is used m times here, i$.$e$.,$ X$**8=(($X$**2)**2)**2,$ because $8=2**3].$