 # Exponential Function Calculator

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The exponential function calculator can calculate a number answer from the exponent-base pair that's plugged in. This can be perfect for finding the final answer to a problem, checking your work, or simply seeing what number is being represented by an exponent.

The rules of exponents can be a bit confusing, especially when you're first learning. On this page, we are going over everything you need to know about exponents as well as how to use our calculator to make your life a lot easier.

## Why use an exponent calculator?

Our calculator can help you if you're struggling with this topic and make it easier to work through problems.

Once you get the rules of exponents straight, many math and science problems can be made a lot more simple to figure out. Plus, it doesn't hurt to use a calculator for extra help, especially as you're learning.

You can also use this tool to check things like scientific notation, which uses 10n as a way to represent both small and large numbers.

## What is an exponent?

An exponent represents a number that indicates how many times the base number is multiplied by itself. This is a bit wordy and confusing, so let's look at what that means.

Let's say we have a base number "a" with the exponent "n". That would look something like this: a (n). The exponent here is "n" and that would indicate how many times you would multiply the integer "a" by "a".

### Example

We have a base number 5 with an exponent 3. This would work out like this:

53

= 5 * 5 * 5

= 125

### Uses

Exponential functions are found in many disciplines including mathematics, physics, biology, and chemistry.

They can be used to make equations simpler, to portray extremely small and/or extremely large numbers, and to display scientific data more clearly.

#### Example

Take the number 1,000,000,000,000.

It is bulky and annoying to write out, especially if you have to use it over and over for a particular equation or problem. For others, counting the zeros can be confusing.

So instead of writing 1,000,000,000,000, you could instead write 1012 to represent the same thing in a much cleaner way.

## What are the rules of exponents?

You'll often find exponents within equations and calculations being added, subtracted, divided, multiplied, etc. In these cases, you need to know how to deal with exponents and how these equations will affects the exponents.

These are called the "rules of exponents." Here are the most common ones you need to know.

When you're adding numbers with exponents, you take the exponent of the bases first and then add the results of those products. Here's a step-by-step example:

5(2) + 6(3)

= (5*5) + (6*6*6)

= 25 + 216

= 241

If you are adding exponents that have the same base number, you can simplify it like this:

a(n) + a(n)

= 2a(n)

### Subtracting Exponents

Just as with adding, when you're subtracting numbers with exponents, you take the exponent of the base numbers first and then subtract the results of those products. For example:

7(4) - 3(5)

= (7*7*7*7) - (3*3*3*3*3)

= 2,401 - 243

= 2,158

### Multiplying Exponents

Sometimes, you'll see exponents with the same base number multiplied. In this case, you add together the exponents. This is called the product rule.

This looks like this:

a(m) * a(n)

= a(m+n)

Here's an example problem:

10(3) * 10(2)

= 10(3+2)

= 10(5)

= 100,000

You might also find a situation where bases being multiplied are taken to the same exponent like this:

(a * c)n

In this case, you would apply the exponent to each of the bases individually then multiply the results of those products, like this:

= a(n) * c(n)

### Dividing Exponents

Dividing two exponents that share the same base can be simplified by subtracting the exponents. This is called the quotient rule.

Here it is visually so you can understand it a bit better:

a(m) / a(n)

= a(m-n)

The only stipulation here is that the base cannot be equal to zero (you cannot divide by 0).

Similar to the multiplication rule, if you have two bases being divided that are taken to the power of n, you apply that n exponent to both bases, then divide. This looks like this:

(a / c)n

= (a(n)) / (c(n))

### The Exponent of an Exponent

Taking an exponent to the power of another exponent can be simplified by multiplying the two exponents together. This is called the power rule, and it looks like this:

(a(m))n

= a(mn)

Here's an example:

(8(2))3

= 8(2*3)

= 85

= 32,768

### Negative Exponents

When you have an exponent that's negative, this means you get the reciprocal of the base raised to that power. This is a bit wordy, so let's look at what this looks like:

a(-n)

= 1/(a(n))

However, in this case, the base cannot be 0. This would result in dividing by 0, which cannot be done.

### Fraction Exponents

If you have an exponent that's a fraction that has a numerator of 1 and a denominator of "n", you take the nth root of the base number.

For example, if you had 16(1/2), you would take the square root of 16 to get an answer of 4.

If you had 125(1/3), you would take the cube root of 125, which would give you an answer of 5.

### Exponent as 1 or 0

Any integer to the power of 1 will simply give you that integer.

101 = 10

1671 = 167

01 = 0.

Any integer taken to the 0th power will give you an answer of 1.

100 = 1

1670 = 1

00 = 1.

## Final thoughts?

While the rules and uses of exponents might seem confusing in words, they're simple once you start applying them to actual coursework.

Practicing these equations and understanding the rules of exponents is crucial for an education in science and math, so we hope this guide has helped you make sense of it.

You can also use our other free online calculators to help you with quadratic equations and other difficult coursework.