Exponential Form Calculator

An integer can be expressed as a product of primes through prime factorization. For example, 250 can be written as:

We can use the exponential form to express this more concisely:

We say that is the exponential form of .

Writing the number in the exponential form retains the vital information (the prime factors) while saving space. If you want to learn how to prime factorize a number, head to our prime factorization calculator.

Since we depend on prime factorizing to write a number this way, we can only express non-zero whole numbers in the exponential form. And of course, since prime numbers' only factors are themselves, their prime factorizations are themselves, too!

❗ Exponential form and exponential notation are different. Exponential notation is similar to the exponential form but doesn't rely on prime factorization. Exponential notation is a way to represent any number in a more accessible format for calculations. Head to our exponential notation calculator to learn more.

A logarithmic number can be converted into its corresponding exponential form due to their relation:

where:

• — The base;
• — The exponent;
• — A number; and
• — Euler's number.

🙋 To learn more about logarithms, visit our log calculator.

For example, consider . We can convert to exponential form by raising to both sides:

Consider another example, , which we can convert by raising to both sides:

Calculating exponential to logarithm form is basically the inverse of what we did in the last section.

For example, consider , which we can convert by applying on both sides:

Our exponential form calculator is straightforward to use:

1. Select what conversion you wish to perform. You can ask our calculator to:

   • Write the exponential form of a whole number;
   • Convert log to exponential form; or
   • Convert exponential to log form.

2. Enter the whole number you wish to convert to exponential form, and our calculator will do the rest.

3. To convert from log form to exponential form ():

   • Enter the logarithm base (b) along with the number (c). The calculator converts it to exponential form and gives you the result.

   • Tip: If base , enter e in the field.

4. To convert from exponential form to log form () to log form:

   • Enter the base (b) along with the exponent (a). Our tool will calculate the logarithm form from the exponential form.

   • Tip: If base , enter e in the field.