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- Raises any base to any power: bⁿ.
- Handles negative exponents (2⁻³) and decimal exponents (9^0.5).
- Shows repeated multiplication steps and the result in scientific notation.
- Warns about undefined cases such as 0 to a negative power.
How to use the exponent calculator
Enter the base
The number being multiplied, such as 2.
Enter the exponent
How many times to multiply it. It can be negative or a decimal.
Read the result
You get the answer, its scientific notation and its reciprocal.
Follow the steps
For small whole exponents the calculator writes out the multiplication.
How exponents work
Exponent rules
bⁿ = b × b × … × b (n times)
b⁰ = 1
b⁻ⁿ = 1 ÷ bⁿ
b^(1/n) = ⁿ√b
Decimal exponents are worked out as e^(n × ln b), which is why a negative base needs a whole-number exponent for a real answer.
Combining powers
bᵐ × bⁿ = bᵐ⁺ⁿ
bᵐ ÷ bⁿ = bᵐ⁻ⁿ
(bᵐ)ⁿ = bᵐⁿ
Example 1: 2¹⁰
A whole-number exponent.
- 2¹⁰ 1,024
- Scientific notation 1.024 × 10³
Powers of 2 are everywhere in computing: 2¹⁰ bytes is one kibibyte.
Example 2: negative and decimal exponents
- 2⁻³ 1 ÷ 2³ = 0.125
- 9^0.5 √9 = 3
- 27^(1/3) ∛27 = 3
- (−2)³ −8
An odd power of a negative number stays negative, while an even power is positive.
Example 3: growth over time
Something growing by 5% a year for 10 years.
- 1.05¹⁰ about 1.6289
- Meaning about 62.89% total growth
This is the same maths behind compound interest.
Where an exponent calculator helps
Algebra and homework
Check powers, negative exponents and roots written as fractional powers.
Compound growth
Work out growth factors such as 1.05¹⁰ for savings, prices or populations.
Science and engineering
Handle powers of ten and very large or very small numbers.
Computing
Find powers of 2 for memory sizes, colour depths and binary values.
Write huge results compactly with the scientific notation calculator, find roots with the square root calculator, and see exponents at work on money in the compound interest calculator.
Exponent calculator FAQ
What is an exponent?
An exponent tells you how many times to multiply a number by itself. In 5³, the base is 5 and the exponent is 3, so 5³ = 5 × 5 × 5 = 125.
What does a negative exponent mean?
It means take the reciprocal. b⁻ⁿ = 1 ÷ bⁿ, so 2⁻³ = 1/8 = 0.125.
Why is any number to the power 0 equal to 1?
Because bⁿ ÷ bⁿ = b⁰, and any non-zero number divided by itself is 1.
What is a fractional exponent?
It is a root. b^(1/2) is the square root of b and b^(1/3) is the cube root.
Why can a negative base not have a decimal exponent?
Something like (−8)^0.5 would be the square root of a negative number, which has no real answer. The calculator asks for a whole-number exponent instead.
How large a result can it show?
Up to about 1.8 × 10³⁰⁸. Very large or very small answers are shown in scientific notation.