Davided.

Exponent Calculator

Raise any number to a power — including negative and fractional exponents, with step-by-step expansion for integer powers and clean handling of 0⁰, division-by-zero, and complex-root edge cases.

✓ Last reviewed: Sources: OpenStax Algebra 1 — 5.1.3 Using the Zero Exponent Property and Negative Exponents

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The number you're raising to a power.

The power to raise the base to (can be negative or fractional).

Advanced options

How many decimal places to show for non-exact results.

Your result

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Exponent calculator: whole, negative and fractional powers

The Davided exponent calculator works out aᵇ for any base and any exponent — not just a straightforward “2 to the power of 10,” but negative exponents, fractional exponents, zero, and the most argued-over edge case in algebra: 0⁰. Enter a base and an exponent, and the result appears instantly — as a decimal, and for small whole-number exponents, also as a fully worked-out multiplication.

That worked-out step is the calculator’s main edge over plugging numbers into a plain scientific calculator: instead of just a number, you also see that 2⁴ = 2×2×2×2 = 16. On top of that, it correctly handles the cases that trip up a lot of online tools — a negative exponent (2⁻³ = 1/8), a fractional exponent read as a root (16^0.5 = √16 = 4), and a negative base raised to a fractional power, where the answer is sometimes real (−8 to the power of 1/3) and sometimes doesn’t exist (−8 to the power of 1/2) — the calculator tells these two apart instead of just failing on any negative base.

It’s built for algebra homework, checking exponent arithmetic by hand, scientific and engineering calculations (exponential notation, exponential growth), and any “what is X to the power of Y” question that’s faster to answer with a calculator than on paper.

How to use the exponent calculator

  1. Enter the base. The number being raised to a power — whole, decimal, zero, or negative.
  2. Enter the exponent. Positive, negative, zero, or fractional (0.5 for a square root, 1/3 for a cube root, and so on).
  3. Read the result. For small positive whole-number exponents you also get the multiplication spelled out (like “2×2×2×2 = 16”); for a fractional exponent, the equivalent root is shown alongside.
  4. Adjust precision if needed. Open Advanced options to change how many decimal places are shown — the default is 6.

Two situations produce no result instead of a number: a base of 0 with a negative exponent (division by zero), and a negative base with a fractional exponent that has an even denominator (a complex, not real, result) — more on both below.

How the calculator works

Positive whole-number exponents

aᵇ for a positive whole number b means multiplying a by itself b times: 2⁴ = 2×2×2×2 = 16. The calculator shows this multiplication spelled out for positive whole-number exponents in a reasonable range (roughly up to 10) — beyond that, the chain of multiplication gets too long to be useful, so you just see the result.

The zero exponent

Any nonzero number raised to the power of 0 equals 1: 7⁰ = 1. That’s a definition, not a special case needing proof — it follows from dividing two equal powers of the same number (a³/a³ must equal a⁰), and any number divided by itself is 1.

Negative exponents

a⁻ⁿ = 1/aⁿ for a nonzero: 2⁻³ = 1/2³ = 1/8 = 0.125. A negative exponent doesn’t flip the sign of the result — it flips the number into a fraction. The exception is a base of 0 with a negative exponent, which means dividing by zero (0⁻² = 1/0² = 1/0), so there’s no real result — the calculator flags this instead of showing infinity as if it were an answer.

Zero raised to a power

0 raised to any positive power is 0 (0⁵ = 0). The exception is 0⁰: by algebraic convention, 0⁰ = 1 — this convention keeps many formulas simple (the binomial theorem, for one) and matches the general rule a⁰ = 1 used for every other base. In calculus, 0⁰ is sometimes treated as indeterminate instead, because the limiting value depends on how the base and exponent each approach zero. The calculator shows 1, with a note about the convention — it’s not an error, just a value defined by agreement rather than by multiplication.

a^(m/n) = ⁿ√(aᵐ) — the numerator of the fraction is a power, the denominator is a root. When m is 1, that’s just an nth root: 16^(1/2) = √16 = 4, and 8^(1/3) = ∛8 = 2. That’s the exact same value you’d get from the square root calculator by setting the matching root degree — both tools compute the same operation, just written differently.

When the base is negative, the outcome depends on the denominator of the exponent (in lowest terms). If the denominator is odd, a real result exists: (−8)^(1/3) = ∛−8 = −2, because (−2)³ = −8. If the denominator is even, no real result exists: (−8)^(1/2) is equivalent to √−8, and no real number squares to a negative value. The calculator tells these two cases apart instead of rejecting every negative base outright.

Very large or very small results, and precision

Floating-point numbers have limits — above a certain size (say, 10⁴⁰⁰), a result no longer fits the number format, and the calculator shows “result too large to display” instead of a number; that’s a limit of representation, not a calculation error. For irrational results (like √2), the calculator rounds to a fixed number of decimal places, 6 by default, adjustable from 0 to 10 in Advanced options. An exact result (like 2⁴ = 16) is always shown without any rounding.

Step-by-step examples

Example 1: a whole-number power, spelled out — 2⁴

2⁴ = 2×2×2×2 = 4×2×2 = 8×2 = 16 exactly.

Example 2: a negative base with a whole-number exponent — (−3)³ and (−3)⁴

(−3)³ = (−3)×(−3)×(−3) = 9×(−3) = −27 (odd exponent, so a negative result). (−3)⁴ = (−3)×(−3)×(−3)×(−3) = 9×9 = 81 (even exponent, positive result). The sign of the result depends only on whether the exponent is odd or even, not on its size.

Example 3: a negative exponent — 2⁻³

2⁻³ = 1/2³ = 1/8 = 0.125 exactly.

Example 4: zero raised to different powers — 0⁵, 0⁻² and 0⁰

0⁵ = 0 (zero base, positive exponent). 0⁻² has no result — it means dividing by zero (0⁻² = 1/0² = 1/0). 0⁰ = 1, shown with a note about the convention — this is an agreed-upon algebraic value, not a result derived from multiplication.

Example 5: a fractional exponent as a root — 16^0.5 and 2^0.5

16^0.5 = √16 = 4 exactly — the same value you’d get from the square root calculator for √16. For a number without a clean root: 2^0.5 = √2 ≈ 1.414214 (6 decimal places).

Example 6: a negative base with a fractional exponent — (−8)^(1/3) versus (−8)^0.5

(−8)^(1/3) = ∛−8 = −2 (check: (−2)³ = −8) — the exponent’s denominator (3) is odd, so a real result exists. (−8)^0.5 has no real result — it’s equivalent to √−8, and the denominator (2) is even, which gives no real answer for a negative base.

Example 7: a result beyond floating-point range — 10⁴⁰⁰

10⁴⁰⁰ exceeds the largest number a standard double-precision floating-point value can hold. The calculator shows a “result too large to display” warning instead of attempting to render a specific digit string — the result exists mathematically, it just doesn’t fit the number format.

Frequently asked questions

What is 2 to the power of 10?

2 to the power of 10 equals 1,024. That comes from spelling out 2¹⁰ = 2×2×2×2×2×2×2×2×2×2 — multiplying 2 by itself ten times, which runs 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024. It’s one of the most-cited powers of two because it equals 1 kibibyte (1,024 bytes) in computing.

How do you calculate a negative exponent?

Flip the base into a fraction and drop the negative sign: a⁻ⁿ = 1/aⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125. The negative sign on the exponent doesn’t make the result negative — it tells you to take the reciprocal of the positive-exponent version.

What does a fractional exponent mean?

A fractional exponent writes a root as a power: a^(1/n) is the same as the nth root of a, so 16^(1/2) = √16 = 4. More generally, a^(m/n) = ⁿ√(aᵐ) — the numerator tells you what power to raise the number to, the denominator tells you which root to take of it. It’s the exact same operation the square root calculator computes, just written in exponent form.

What is any number to the power of 0?

Any nonzero number raised to the power of 0 equals 1 — 7⁰ = 1, and even (−5)⁰ = 1. That follows from the rule for dividing powers: aⁿ/aⁿ = aⁿ⁻ⁿ = a⁰, and any nonzero number divided by itself equals 1. The one exception to this rule is a base of 0 itself — see the next question.

What is 0 to the power of 0?

By algebraic convention, 0⁰ = 1 — this is an agreed-upon value, not something derived from multiplication, since “multiplying zero by itself zero times” has no natural meaning. The convention keeps formulas like the binomial theorem simple, and it matches the rule a⁰ = 1 that holds for every other base. In calculus, 0⁰ is sometimes treated as indeterminate instead, because the value of a limit depends on exactly how the base and exponent each approach zero.

How do you raise a fraction to a power?

Raise the numerator and the denominator to that power separately: (a/b)ⁿ = aⁿ/bⁿ. For example, (1/2)³ = 1³/2³ = 1/8 = 0.125 — the same value you’d get by entering 0.5 as the base and 3 as the exponent in this calculator, since 1/2 and 0.5 are the same number.

Can you raise a negative number to a fractional exponent?

Sometimes — it depends on the denominator of the exponent once it’s reduced to lowest terms. If the denominator is odd, a real result exists: (−8)^(1/3) = −2, because (−2)³ = −8. If the denominator is even, there’s no real result: (−8)^(1/2) is equivalent to √−8, and no real number squares to a negative value, so there’s no solution among the real numbers.

How do you calculate a power without a scientific calculator?

For a whole-number exponent, just multiply the base by itself that many times (2⁴ = 2×2×2×2). For a fractional exponent, use the “^” or “xʸ” function if your calculator has one — 16^0.5 is entered as 16 ^ 0.5. Without a power function or a way to multiply in a loop, a fractional exponent is hard to work out by hand with any real precision — that’s exactly the gap this calculator fills.

What’s the difference between an exponent and a power?

They’re two different parts of the same notation: in 2⁴, the number 2 is the base, 4 is the exponent, and the whole expression 2⁴ (which equals 16) is the power. In everyday speech “exponent” and “power” often get used interchangeably for the whole operation (“raising to a power,” “exponentiation”), but strictly speaking the exponent is just the superscript, while the power is the result of the operation.

Sources