Need to calculate a number raised to a power? Our free Exponent Calculator makes it quick and easy. Enter a base number and an exponent to calculate the result instantly. It works with whole numbers and decimals, including positive, negative, and fractional exponents.
Exponent Calculator
How to Use the Exponent Calculator
Using the Exponent Calculator is easy. Enter the base number and the exponent, then click Calculate.
For example, if you enter 2 as the base and 5 as the exponent, the calculator works out:
2⁵ = 32
The calculator also supports decimal and negative exponents.
What Is an Exponent?
An exponent tells you how many times a number is multiplied by itself.
For example:
2³ = 2 × 2 × 2 = 8
Here, 2 is the base and 3 is the exponent.
Exponents are also sometimes called powers or indices.
Exponent Formula
The basic exponent formula is:
aⁿ = a × a × a …
where a is the base and n is the exponent.
For example:
5⁴ = 5 × 5 × 5 × 5 = 625
Positive Exponents
A positive exponent means the base is multiplied by itself the number of times indicated by the exponent.
For example:
3² = 3 × 3 = 9
And:
4³ = 4 × 4 × 4 = 64
Exponent of 1
Any non-zero number raised to the power of 1 remains the same.
For example:
7¹ = 7
25¹ = 25
Exponent of 0
Any non-zero number raised to the power of 0 equals 1.
For example:
8⁰ = 1
100⁰ = 1
The expression 0⁰ is treated separately in mathematics and is not calculated by this tool.
Negative Exponents
A negative exponent represents the reciprocal of the corresponding positive power.
For example:
2⁻³ = 1/2³ = 1/8
So:
2⁻³ = 0.125
Another example:
10⁻² = 1/100 = 0.01
Fractional Exponents
A fractional exponent can represent a root.
For example:
9¹ᐟ² = √9 = 3
Similarly:
8¹ᐟ³ = ∛8 = 2
Fractional exponents are useful when working with roots and more advanced mathematical expressions.
Exponent Calculator Examples
Example 1: 2 to the Power of 5
2⁵ = 32
Example 2: 10 to the Power of 3
10³ = 1,000
Example 3: 5 to the Power of 2
5² = 25
Example 4: Negative Exponent
4⁻² = 1/16 = 0.0625
Example 5: Decimal Base
If the base is 2.5 and the exponent is 2:
2.5² = 6.25
Exponents and Square Roots
Exponents and roots are closely related.
A square root can be written as a fractional exponent:
√x = x¹ᐟ²
For example:
√25 = 25¹ᐟ² = 5
This relationship is particularly useful when working with algebra and higher-level mathematics.
Common Exponent Rules
Some basic exponent rules make calculations easier.
Same base multiplication:
aᵐ × aⁿ = aᵐ⁺ⁿ
Same base division:
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power of a power:
(aᵐ)ⁿ = aᵐⁿ
These rules are commonly used when simplifying expressions with exponents.
Frequently Asked Questions
What is an exponent?
An exponent tells you how many times a number is used as a factor in multiplication.
What is the difference between a base and an exponent?
The base is the number being raised to a power. The exponent tells you the power to which the base is raised.
What is 2 to the power of 5?
2⁵ = 32.
What happens when the exponent is zero?
Any non-zero number raised to the power of zero equals 1.
Can I use a negative exponent?
Yes. The calculator supports negative exponents.
Can I use decimal exponents?
Yes. You can enter decimal values for the exponent. Some decimal exponents may produce results that are not real numbers for certain negative bases.
Is an exponent the same as a power?
The terms are closely related. For example, in 2³, 3 is the exponent and 2³ is a power of 2.
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