Exponent Calculator
Raise any number to any power.
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An exponent tells you how many times to multiply a number by itself. Enter a base and a power to get the exact result — this calculator handles positive, negative, and fractional exponents, and shows the expanded multiplication for whole-number powers.
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How Exponents Work — The Quick Answer
A positive whole exponent means repeated multiplication. A negative exponent means one divided by the positive power. A fractional exponent is a root. And anything (except 0) to the power 0 is 1.
Shortcut
bⁿ = b × b × … (n times) | b⁻ⁿ = 1 ÷ bⁿ | b^(1/n) = ⁿ√b | b⁰ = 1
Fact-Checking Claims You May Have Seen Online
A negative exponent makes the result negative
False
A negative exponent means a reciprocal, not a negative number. 2⁻² = 1 ÷ 2² = 1 ÷ 4 = 0.25 — still positive.
Anything to the power of zero is zero
False
Any non-zero number to the power 0 equals 1, not 0. This keeps the laws of exponents consistent (bⁿ ÷ bⁿ = b⁰ = 1).
Exponents at a glance
| Expression | Meaning | Result |
|---|---|---|
| 2^10 | 2 multiplied by itself 10 times | 1,024 |
| 5^3 | 5 × 5 × 5 | 125 |
| 2^-2 | 1 ÷ (2 × 2) | 0.25 |
| 9^0.5 | the square root of 9 | 3 |
| 10^0 | anything (non-zero) to the power 0 | 1 |
A fractional exponent is a root: b^(1/2) is the square root, b^(1/3) is the cube root. A negative base with a fractional exponent (like (−8)^0.5) has no real value, so it isn't defined here.
How It Works
The Rules of Exponents
What each kind of exponent means
Formula
Positive: bⁿ = b × b × … × b (n factors) Zero: b⁰ = 1 (for b ≠ 0) Negative: b⁻ⁿ = 1 ÷ bⁿ Fractional: b^(1/n) = the nth root of b
Variables
Positive whole exponent
Repeated multiplication. 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. The base is the number; the exponent counts the factors.
Negative exponent
A reciprocal: flip the base and make the exponent positive. 2⁻³ = 1 ÷ 2³ = 1 ÷ 8 = 0.125. The result stays positive for a positive base.
Fractional exponent
A root. b^(1/2) is the square root, b^(1/3) the cube root. More generally b^(m/n) is the nth root of b, raised to the m-th power.
Note: These rules combine: 8^(2/3) means the cube root of 8 (which is 2), squared — giving 4.
Worked Example
2^10, 2^-2 and 9^0.5
2^10
2 multiplied by itself 10 times: 2×2×2×2×2×2×2×2×2×2 = 1,024.
2^-2
A negative exponent is a reciprocal: 1 ÷ 2² = 1 ÷ 4 = 0.25.
9^0.5
A ½ exponent is the square root: √9 = 3.
Reference Guide
| unit | value | note |
|---|---|---|
| 2^10 | 1,024 | repeated multiplication |
| 5^3 | 125 | 5 × 5 × 5 |
| 2^-2 | 0.25 | reciprocal |
| 9^0.5 | 3 | square root |
Key Features
Last updated: October 5, 2026
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Frequently Asked Questions
What does a negative exponent mean?
A negative exponent means the reciprocal of the positive power — one divided by the base raised to that power. For example 2⁻² = 1 ÷ 2² = 1 ÷ 4 = 0.25. The answer is not negative; it's a fraction (for a base bigger than 1).
Why is any number to the power of zero equal to 1?
Because of how exponents divide: bⁿ ÷ bⁿ equals 1, and by the subtraction rule it also equals b^(n−n) = b⁰. For both to agree, b⁰ must be 1. This holds for every non-zero base. (0⁰ is a special, debated case.)
What is a fractional exponent?
A fractional exponent is a root. Raising a number to the power 1/2 gives its square root, 1/3 gives its cube root, and so on. For example 9^(1/2) = 3 and 27^(1/3) = 3. A power like 8^(2/3) means the cube root of 8, squared, which is 4.
Can I raise a negative number to a power?
Yes for whole-number exponents — (−2)³ = −8, and (−2)² = 4. But a negative base with a fractional exponent, such as (−8)^0.5, has no real value (the square root of a negative number is imaginary), so this calculator reports it as undefined.