Question

Devise an algorithm to compute xⁿ, where xis a real number and nis an integer. [Hint:First give a procedure for computing xⁿwhen nis nonnegative by successive multiplication by x, starting with 1. Then extend this procedure, and use the fact that x⁻ⁿ=1/xⁿto compute xⁿwhen nis negative.]

Short answer

The required algorithm is designed.

Step-by-step solution

Step 1

The algorithm is "power" and the input is a real number x and integer n.



procedure power ( x : real number, n: integer)

Step 2

We initially define the variable k as 1.

Step 3

Substitutingk =1

If nis nonzero,

Then for every integer ibetween 1 and∣n∣multiplying kby x(resulting in the i^thpower of x ).

Step 4

if n≠0

Then

i=0 to∣n∣



k= k⋅

Step 5

If nis a negative integer then,

Substituting x⁻¹= $\frac{1}{x^n}$

Step 6

then

k = $\frac{1}{k}$

Step 7

Return the variable k which will contain the n^thpower at the end of the loop.

Return k.

Step 8

Combining all the step for procedure power

( x : real number)

( y: integer)

 K =1

Step 9

If n≠ 0, then

For i=0 to∣n∣



K =k⋅x



If n<0,

then

k= $\frac{1}{k}$

Step 10

Return

k.