Exponent Calculator
Compute a base raised to an integer, negative or fractional power, with the power rules, special cases like 0 and negatives, and examples such as 2¹⁰ and 9^0.5.
Results
Result
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Educational estimates · not financial advice · free, no signup
Formula / how it works
aᵇ = a multiplied by itself b times for positive integers. a⁻ᵇ = 1 ÷ aᵇ. a^(1/2) = √a. a⁰ = 1 for a ≠ 0. Fractional powers of negative bases are not real numbers.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
An exponent tells you how many times to multiply a base by itself. 2¹⁰ is ten twos multiplied together, which is 1,024. Negative exponents mean reciprocals and fractional exponents mean roots, so 9^0.5 is the square root of 9. Exponents show up in compound interest, scientific notation, growth models and computing. This calculator raises any base to any exponent. Very large results overflow to infinity and tiny results approach zero. A negative base with a fractional exponent has no real answer, and zero to a negative power is undefined. For growth problems, even small exponents on a base slightly above one produce large changes over time.
When to use / who it helps
- You need a power for homework or an equation.
- You are calculating compound growth, for example 1.07¹⁰.
- You want a root through a fractional exponent.
- You are converting scientific notation.
- You are checking binary powers.
How to use
Steps
- Enter the base.
- Enter the exponent.
- Read the result.
- For roots, use exponents like 0.5 or 1/3 as decimals.
- For compound growth, enter 1 plus the rate as the base.
- Check negative bases carefully.
How to interpret results
- Exponents above 1 grow the base; between 0 and 1 they take roots.
- Negative exponents give reciprocals.
- Any non-zero base to the power 0 is 1.
- Large exponents can exceed the calculator's range.
- Even powers of negative bases are positive.
Common mistakes & gotchas
- Confusing (−2)² = 4 with −2² = −4 when working by hand.
- Entering a fractional exponent for a negative base.
- Confusing a^b with a×b.
- Forgetting that a⁰ = 1.
- Rounding intermediate results.
Worked example
Worked example — 2¹⁰, 2⁻³, 9^0.5 and 1.07¹⁰
- 2¹⁰ = 1,024.
- 2⁻³ = 1 ÷ 2³ = 1 ÷ 8 = 0.125.
- 9^0.5 = √9 = 3.
- 1.07¹⁰ ≈ 1.967, which means 7% growth for 10 years nearly doubles an amount.
Result: 2¹⁰ = 1,024.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
aᵇ = a multiplied by itself b times for positive integers. a⁻ᵇ = 1 ÷ aᵇ. a^(1/2) = √a. a⁰ = 1 for a ≠ 0. Fractional powers of negative bases are not real numbers.
Frequently asked questions
What does an exponent mean?
How many times the base is multiplied by itself.
What is a number to the power 0?
1, if the base is not zero.
What is a negative exponent?
The reciprocal of the positive power.
What is a fractional exponent?
A root, such as 0.5 for a square root.
Can I raise a negative number to a fractional power?
Not in the real numbers in general.
How is this used in finance?
Compound growth uses (1 + rate) raised to the number of periods.