$2.$a$).$ Design an Algorithm and Develop a C program to calculate the power of a number $($i$.$e$.,$ x

n

$)$ using

a loop.

b$)$ Develop a C program to calculate and print the power of numbers in a given range. For example,

calculate i

j

for i from $1$ to $5$ and j from $1$ to $3.$

c$)$ Create a number n is constructed by summing the powers of natural numbers, where each number is

raised to the power of $2($i$.$e$.,1^2,2^2,3^2,...)$ until the sum reaches or exceeds $500.$The construction must

stop as soon as the cumulative sum of these powers becomes a $3-$digit number $($i$.$e$.,$ reaches or exceeds

$500).$

d$)$ Construct three integer numbers x$1,$ x$2$ using numbers generated by a while loop $($starting from $1)$ in

such a way that:

i$.$ x$1$ is constructed only from the squares of even numbers generated by the while loop, and its

construction must stop as soon as it becomes a $4-$digit number.

ii$.$ x$2$ is constructed from the cubes of odd numbers generated by the while loop, and its construction

must stop as soon as it becomes a $4-$digit number.