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Exponent Calculator

Raise any base to any exponent — positive, negative, or fractional — and get the exact value instantly. A negative power gives a reciprocal and a fractional power gives a root.

Enter a base and an exponent (power) to compute baseexponent. Negative and fractional exponents are supported — a negative exponent gives a reciprocal and a fractional exponent gives a root.

Result
1,024

2^10 = 1,024

Exponentiation bⁿ means multiplying the base b by itself n times. A negative exponent is a reciprocal: b⁻ⁿ = 1 / bⁿ. A fractional exponent is a root: b^(1/n) = ⁿ√b. The result is computed with the standard Math.pow function in your browser.

Quick answer

An exponent tells you how many times to multiply the base by itself: 2^10 means ten 2s multiplied together, which equals 1,024. A negative exponent is a reciprocal (5^-2 = 1/25 = 0.04) and a fractional exponent is a root (27^(1/3) = 3, the cube root of 27). This calculator handles all three cases with Math.pow and gracefully flags a negative base with a fractional exponent, which has no real value.

Formula & method

The tool computes base^exponent using JavaScript's Math.pow, which directly supports integer, negative, and fractional exponents. A negative exponent is reported as a reciprocal (b^-n = 1 / b^n) and a non-integer exponent as a root (b^(1/n) = the nth root of b). When the base is negative and the exponent is fractional, Math.pow returns NaN; the tool detects an odd-denominator root (such as (-8)^(1/3) = -2, which is real) and otherwise explains that the result is a complex number. Zero to a negative power is flagged as undefined.

Examples

Example 1: Whole-number power
Input
base 2, exponent 10
Result
1,024
Why
2^10 multiplies ten 2s together: 2×2×2×2×2×2×2×2×2×2 = 1,024.
Example 2: Negative exponent
Input
base 5, exponent -2
Result
0.04
Why
A negative exponent is a reciprocal: 5^-2 = 1 / 5^2 = 1 / 25 = 0.04.
Example 3: Fractional exponent (root)
Input
base 27, exponent 1/3 (0.3333…)
Result
3
Why
27^(1/3) is the cube root of 27, because 3 × 3 × 3 = 27.
Example 4: Square root as a power
Input
base 2, exponent 0.5
Result
≈ 1.4142135624
Why
2^0.5 equals the square root of 2, an irrational decimal shown to 10 places.
Example 5: Power of zero
Input
base 10, exponent 0
Result
1
Why
Any non-zero number raised to the power 0 equals 1.
Example 6: Real root of a negative base
Input
base -8, exponent 1/3
Result
-2
Why
The cube root is an odd-degree root, so (-8)^(1/3) = -2 is a real value even though the base is negative.

When to use this tool

  • Computing compound growth, areas, or volumes where a quantity is raised to a power.
  • Converting between a root and a power — for example finding a cube root as x^(1/3).
  • Evaluating scientific or engineering formulas that use negative or fractional exponents.
  • Checking homework or building intuition for how exponents, reciprocals, and roots relate.

Common mistakes

  • Reading a^b as a × b instead of multiplying the base by itself b times — 2^10 is 1,024, not 20.
  • Expecting a negative result from a negative exponent: 5^-2 is 0.04 (a small positive reciprocal), not a negative number.
  • Assuming every fractional power of a negative base is real — an even-denominator root such as (-4)^0.5 is complex (imaginary), while an odd-denominator root like (-8)^(1/3) is real.
  • Treating 0^0 as 0; by the convention used here (and in most software) it equals 1, while 0 to a negative power is undefined.

Frequently asked questions

What does an exponent mean?

An exponent (or power) tells you how many times to multiply the base by itself. In 2^10 the base is 2 and the exponent is 10, so you multiply ten 2s together to get 1,024.

How does a negative exponent work?

A negative exponent is the reciprocal of the positive power: b^-n = 1 / b^n. For example 5^-2 = 1 / 5^2 = 1 / 25 = 0.04.

What is a fractional exponent?

A fractional exponent is a root. The denominator is the root degree and the numerator is a power, so b^(1/n) is the nth root of b. For instance 27^(1/3) = 3 and 2^0.5 = √2 ≈ 1.41.

Why does a negative base with a fractional exponent give no real answer?

Even-degree roots of a negative number are imaginary, so (-4)^0.5 has no real value. Odd-degree roots are real, however, so this tool returns (-8)^(1/3) = -2.

What is 0 to the power 0?

This calculator follows the common convention that 0^0 = 1, matching what most calculators and programming languages return. Zero raised to a negative power is undefined because it implies dividing by zero.

Is my calculation sent anywhere?

No. Everything is computed locally in your browser with the standard Math.pow function, so nothing is uploaded.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

  • ✓ Free to use
  • ✓ No sign-up required
  • ✓ Runs entirely in your browser — nothing is uploaded.
  • ✓ Formula and method shown above
Last updated: How we calculateReport a correctionDisclaimer

Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.

Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.

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