Need to find the power of a number or solve a simple exponential equation? The free Exponent Calculator from NexCalco makes it easy. Enter a base and exponent to calculate a power instantly, or switch to the equation solver to find a missing exponent. It supports whole numbers, decimals, negative exponents, and equations with one unknown variable.
Exponent Calculator
Calculate a number raised to a power. For example, 5² = 25.
Solve equations with the same base multiplied by itself using different exponents. Enter a variable in exactly one exponent field, such as x, y, or z.
Example: 5^10 × 5^9 = 5^x. Enter 10, 9, and x in the three exponent fields to find x = 19.
How to Use the Exponent Calculator
The Exponent Calculator has two options, depending on what you want to work out.
1. Power Calculator
Enter the base and exponent, then click Calculate to get the result.
For example, enter 2 as the base and 5 as the exponent:
2⁵ = 2 × 2 × 2 × 2 × 2 = 32
You can also use decimal and negative exponents.
2. Solve Exponential Equations
Choose Solve Exponential Equations to find a missing exponent. Enter the base and fill in the three exponent fields, using a variable such as x in exactly one field.
For example:
5ˣ × 5⁵ = 5⁹
Since multiplying powers with the same base means adding their exponents:
x + 5 = 9
Therefore, x = 4.
What Is an Exponent?
An exponent tells you the power to which a number is raised. It shows how many times the base is used as a factor in multiplication when the exponent is a positive whole number.
For example:
2³ = 2 × 2 × 2 = 8
Here, 2 is the base, and 3 is the exponent. Exponents are also commonly called powers or indices.
Exponent Formula
The basic formula for a power is:
aⁿ
Where:
- a is the base.
- n is the exponent.
- aⁿ is the result of raising the base to the exponent.
For example:
5⁴ = 5 × 5 × 5 × 5 = 625
Types of Exponents
Positive Exponents
A positive whole-number exponent means multiplying the base by itself the indicated number of times.
Examples:
3² = 3 × 3 = 9
4³ = 4 × 4 × 4 = 64
Exponent of 1
Any number raised to the power of 1 equals the number itself.
7¹ = 7
25¹ = 25
Exponent of 0
Any non-zero number raised to the power of zero equals 1.
8⁰ = 1
100⁰ = 1
The expression 0⁰ is treated separately in mathematics, so this calculator does not evaluate it using the usual zero-exponent rule.
Negative Exponents
A negative exponent represents the reciprocal of the corresponding positive power.
For example:
2⁻³ = 1 ÷ 2³ = 1/8 = 0.125
Another example:
10⁻² = 1 ÷ 10² = 0.01
Fractional and Decimal Exponents
A fractional exponent can represent a root. For example:
9¹ᐟ² = √9 = 3
8¹ᐟ³ = ∛8 = 2
Decimal exponents work similarly, although the result may be a decimal rather than a whole number.
For instance:
16⁰·⁵ = 4
Exponent Calculator Examples
Here are a few examples you can try with the Power Calculator.
| Calculation | Result |
|---|---|
| 2⁵ | 32 |
| 10³ | 1,000 |
| 5² | 25 |
| 4⁻² | 0.0625 |
| 2.5² | 6.25 |
| 16⁰·⁵ | 4 |
These examples show how the result changes with different bases and exponents.
How to Solve Exponential Equations
When two powers have the same positive base, excluding 1, their exponents can be equated when the powers are equal.
For example:
5ˣ × 5⁵ = 5⁹
First, use the multiplication rule for powers with the same base:
5ˣ⁺⁵ = 5⁹
Next, equate the exponents:
x + 5 = 9
Subtract 5 from both sides:
x = 9 − 5 = 4
The answer is x = 4.
The equation solver can also work when the unknown appears in the second exponent or on the right-hand side.
For example:
5¹⁰ × 5⁹ = 5ˣ
Add the known exponents:
x = 10 + 9 = 19
And for:
5⁹ × 5ˣ = 5⁵
Subtract 9 from 5:
x = 5 − 9 = −4
Common Exponent Rules
These rules are useful for simplifying expressions and solving equations.
Multiplication with the same base
aᵐ × aⁿ = aᵐ⁺ⁿ
Add the exponents when multiplying powers with the same base.
Division with the same base
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Subtract the denominator’s exponent from the numerator’s exponent, provided the division is defined.
Power of a power
(aᵐ)ⁿ = aᵐⁿ
Multiply the exponents.
Power of zero
a⁰ = 1, for a ≠ 0.
Negative exponent
a⁻ⁿ = 1/aⁿ, for a ≠ 0.
Exponents and Square Roots
Exponents and roots are closely related. A square root can be expressed as a fractional exponent:
√x = x¹ᐟ²
For example:
√25 = 25¹ᐟ² = 5
Similarly, a cube root can be written as an exponent of one-third:
∛8 = 8¹ᐟ³ = 2
This relationship is useful in algebra, geometry, and more advanced mathematics.
Frequently Asked Questions
What is an exponent?
An exponent indicates the power to which a base is raised. For a positive whole-number exponent, it tells you how many times the base 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, while the exponent indicates the power. In 2⁵, for example, 2 is the base and 5 is the exponent.
What is 2 to the power of 5?
2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
What happens when the exponent is zero?
Any non-zero base raised to the power of zero equals 1.
Can I calculate negative exponents?
Yes. Enter a negative exponent in the Power Calculator. For example, 2⁻³ equals 0.125.
Can I enter decimal exponents?
Yes. The calculator accepts decimal exponents. However, certain combinations, such as a negative base raised to a non-integer exponent, may not produce a real-number result.
Can this calculator solve for a missing exponent?
Yes. Select Solve Exponential Equations and enter a variable such as x in exactly one of the three exponent fields. The calculator solves equations of the form aᴬ × aᴮ = aᶜ when one exponent is unknown.
Is an exponent the same as a power?
The terms are closely related. In 2³, the number 3 is the exponent, while 2³ represents 2 raised to the third power.
Is the Exponent Calculator free?
Yes. You can use the NexCalco Exponent Calculator online for free without installing software.
Note: This calculator is intended for general mathematical calculations and simple exponential equations with matching bases.
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