Exponent calculator

Exponential function calculator overview

Our exponents calculator is a handy tool for anyone looking to simplify their calculations of exponents. Whether you're a student or a professional, our exponents solver will become a game-changer for you. The best part? You can use our calculator for free.

This versatile tool can compute the result of exponentiation in a breeze, delivering accurate results every time. But first, let's find out what exponentiation is. In mathematics, it is an operation written as an, in which a is the base and n is the exponent. If n is a positive, exponentiation equates to repeated multiplication of a (the base) n times.

Our calculator accepts negative bases but not imaginary numbers. It can also be used as a fraction exponent calculator since it computes fractional exponents as long as they are in decimal form.

To take advantage of our smart computational tool, you have to follow these simple steps:

Enter the values into two input fields. You can also use e as a base.
Click "calculate" to solve for the third and get precise results in an instant.

With our calculator, it is as simple as that.

Basic rules and laws of exponents

If you're wondering how to use exponents on a calculator, get acquainted with these basic laws and rules of exponentiation:

When multiplying exponents that share the same base, one needs to add the exponents. Our multiplying exponent calculator can come in handy in this case.

aⁿ × a^m = a^(n+m)

2. When dealing with negative exponents, one needs to remove the negative sign by reciprocating the base and raising it to the positive exponent.

a^(-n) =1/aⁿ

3. One needs to subtract the exponents when dividing the exponents with the same base.

a^m/aⁿ= a^{(m - n)}

4. When raising exponents to another exponent, one has to multiply the exponents.

(a^m)ⁿ = a^{(m × n)}

5. When raising multiplied bases to an exponent, one has to distribute the exponent to both bases.

(a × b)ⁿ = aⁿ × bⁿ

6. When raising divided bases to an exponent, one also needs to distribute the exponent to both bases.

(a/b)ⁿ = aⁿ / bⁿ

7. If an exponent is 1, the base stays the same.

a¹ = a

8. If an exponent is 0, the result for any base will always be 1. However, some mathematicians debate 00 as being 1 or unidentified.

a⁰ = 1

Here's an example of this rule:

If aⁿ × a^m = a^(n+m)

Then aⁿ × a⁰ = a⁽ⁿ⁺⁰⁾ = aⁿ

So, the only way for an to stay unchanged during multiplication is if a0 = 1.

9. When dealing with a fractional exponent where the numerator is 1, one has to take the nth root of the base. Here's an example of an exponent that's a fraction where the numerator isn't 1.

a^(1/n)=ⁿ√a

Example:

3^(5/7)= (3^(1/7))⁵=(⁷√3)⁵= 1.17⁵ = 2.19

Please note that our calculator computes fractional exponents entered in decimal form.

10. The rules for exponents with negative bases are basically the same as for their positive counterparts. Negative exponents raised to positive integers are equal to positive ones in magnitude but vary based on their sign. If it is an even, positive integer, the values are equal regardless of the sign of the base. If the exponent is an odd, positive integer, the results will be of the same magnitude but have a negative sign.

The laws for fractional exponents with negative bases are the same as for the positive one. The only difference is the use of imaginary numbers. Please note that our calculator doesn't support imaginary numbers.