You use exponents in r when you have a number that you want to raise to a power. R has two commands that are capable of doing exponents and they both produce exactly the same results. So, deciding which one to use is purely a matter of personal taste. Because these two commands produce the same result you can use whichever one you want.

### Description – Exponents in R

There are two ways of doing exponents in r. The first has the format of x^y where “x” is the number that is going to be raised to the “y” power. This version is the most common way in programming of doing exponents. The second has the format of x**y where “x” is the number that is going to be raised to the “y” power. Each expression works with either a positive or negative exponent. If you would prefer to have a function, you could create a function to raise a number to a power. Regardless of the approach you use, these two expressions will serve your needs.

### Explanation – Exponents in R

Doing exponents in r is related to scientific notation and logarithms. Scientific notation is a convenient way of using exponents to prevent having a lot of digits on the left side of the decimal place. When you are raising a number to the power of an integer, it is simply a matter of multiplying that number by itself the number of times the power the numeric value is being raised to. It gets more complicated when dealing with fractional or negative numbers, however, the basic principle is still the same. One thing to keep in mind is that when the exponent is positive, the result will be greater than one and when it is negative it will be between zero and one.

### Examples – Exponents in R

Here we have several examples using exponents in r. Each of them illustrates different aspects of these commands.

> 2^10

[1] 1024

> 2**10

[1] 1024

This example illustrates the simplest possible way of doing an exponent. We are using both techniques to directly apply an exponent to a value.

> x = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

> x^2

[1] 1 4 9 16 25 36 49 64 81 100

> x**2

[1] 1 4 9 16 25 36 49 64 81 100

In this example, we apply an exponent to a vector. The result is a series of squared values.

> x = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

> y = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

> x^y

[1] 1 4 27 256 3125 46656 823543 16777216 387420489

[10] 10000000000

> x**y

[1] 1 4 27 256 3125 46656 823543 16777216 387420489

[10] 10000000000

In this example, we take the exponent of one vector and raise it to the power of the second. The result here is that each value in the first vector is raised to the power of the corresponding value in the second vector.

> x = data.frame(X = c(1, 2, 3, 4, 5),

+ Y = c(6, 7, 8, 9, 10))

> x^3

X Y

1 1 216

2 8 343

3 27 512

4 64 729

5 125 1000

> x**3

X Y

1 1 216

2 8 343

3 27 512

4 64 729

5 125 1000

In this example, we apply an exponent to a data frame. The result is a data frame of squared values.

> x = data.frame(X = c(1, 2, 3, 4, 5),

+ Y = c(6, 7, 8, 9, 10))

> y = data.frame(X = c(1, 2, 3, 4, 5),

+ Y = c(6, 7, 8, 9, 10))

> x^y

X Y

1 1 46656

2 4 823543

3 27 16777216

4 256 387420489

5 3125 10000000000

> x**y

X Y

1 1 46656

2 4 823543

3 27 16777216

4 256 387420489

5 3125 10000000000

In this example, we take the exponent of one data frame and raise it to the power of the second. The result here is that each value in the first data frame is raised to the power of the corresponding value in the second data frame.

### Application – Exponents in R

When doing exponents with text, a superscript is used denote an exponent. A subscript is used to signify other things. This is one reason formats such as x^y are commonly used in programming. It is reminiscent of the superscript. There are many applications of exponents because they are found all over physics and other sciences. In data science, there are a large number of essential functions that use exponents. They are a necessary part of calculating exponential distributions. Exponentials are an important part of a binomial function. They are an important part of population growth and atomic decay, both of which are statistically expressed by exponential functions. Other examples of important statistical functions that are used in data science include sample variance, the poisson formula, the multinomial formula, and much more. Exponential formulas have so many applications in data science, physics, chemistry, and particularly in pure mathematics that it would be impossible to list all the applications for this simple mathematical process.

When doing exponents in r you have a couple of different commands that run this calculation. They are simple to use and quite logical making them easy to remember. This is a valuable tool whose applications you will never find an end to.