Matlab

# How to Work with Powers and Exponentials in MATLAB

Taking powers and exponentials of any scalar, vector, or multidirectional array is a basic and widely used mathematical operation. We can compute the power of any scalar or array in MATLAB using the ^ operator; however, the exponentials of a scalar or an array can be calculated using the built-in exp() function.

This tutorial is going to discuss different examples of how to work with powers and exponentials of a scalar, matrix, vectors, or an array in MATLAB.

## 1: How to Take Power in MATLAB

Taking power in MATLAB is a useful task regardless of whether you are taking the power of a scalar, array, or matrix, all and all you have to use the ^ operator for this operation. The ^ operator computes any positive, negative, and fractional powers of a number within no time. The ^ operator is a piecewise operator which means it is applied to each element of an array individually using the .^ operator instead. The same case applies to calculating the power in matrices, vectors, and multidirectional arrays as well.

## Example 1: How to Calculate the Power of a Scalar in MATLAB?

This MATLAB code computes the positive, negative, and fractional powers of the given number using the ^ operator.

num = 64;
ans1 = num^2
ans2 = num^(-2)
ans3 = num^(1/2)

## Example 2: How to Calculate the Power of a Square Matrix in MATLAB?

In this example, we calculate the positive, negative, fractional, and element-wise powers of the given square matrix.

A = magic(2);
ans1 = A^3
ans2 = A^(-3)
ans3 = A^(1/3)
ans4 = A.^3

## 2: How to Use Exponentials in MATLAB

Taking exponentials is another common task widely used in MATLAB programming. We can calculate the exponentials of a scalar, vector, matrix, or multidimensional array using the built-in exp() function. This function takes a number or an array as an input argument and provides its calculated exponential in return.

## Syntax

In MATLAB, you can use the exp() function in the following way:

exp(X)

## Example 1: How to Calculate the Exponential of a Scalar in MATLAB?

In this MATLAB code, we use the exp() function to compute the exponential of the given number.

num = 7.9;
exp(num)

## Example 2: How to Calculate the Exponential of an Array in MATLAB?

In this example, we calculate the exponential of the given array using the exp() function in MATLAB.

X = randi(100,4,7,2);
exp(X)

For more details in our guide; how to use the exp() function to find exponential in MATLAB.

# Conclusion

MATLAB is a beneficial programming tool that allows us to perform many tasks. It enables us to compute the powers and exponentials of a scalar or an array using the ^ operator and exp() function, respectively. This guide has provided beginner-level instruction to help users calculate the powers and exponentials in MATLAB for a matrix, vectors, or multi-dimensional arrays.