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Exponent Calculator

Raise a base to a power, or solve for the missing base, exponent, or result. Enter any two of a, n, and a^n. Supports e as the base.

ExampleSample values — edit any field to see your result.

The number being multiplied. Type e for Euler's number, or check Use e as base. Leave blank if this is the unknown — enter any two values.

Replace the base with Euler's number e ≈ 2.71828 (the same as typing e).

How many times to multiply the base. Use a decimal for a fractional power (0.5 for a square root). Leave blank if this is the unknown — enter any two values.

The value of a raised to n. Leave blank if this is the unknown — enter any two values.

Results update as you type.

Solution

2^5 = 32

Estimated result

Base a
2
Exponent n
5
aⁿ
32

Steps

Worked solution
2^5 = 2 × 2 × 2 × 2 × 2
= 32
Solution2^5 = 32

Enter any two of the base, the exponent, and the result to solve a^n. Use a decimal exponent for roots, a negative exponent for reciprocals, or e for Euler's number.

Formula

When n is a positive integer, exponentiation is repeated multiplication:

a^n = a × a × … × a   (n times)

The other common identities this calculator uses:

a^(−n) = 1 / a^n
a^0 = 1
a^1 = a
a^(1/n) = ⁿ√a

To recover a missing exponent, take logarithms: n = log(r) / log(a). To recover a missing base, take the n-th root: a = r^(1/n). Even integer exponents with a positive result have two real bases, ±.

The default 2^5 expands as 2 × 2 × 2 × 2 × 2 = 32. Check Use e as base to compute e^n (e^1 ≈ 2.718281828459).

Examples

Default power

Base 2, exponent 5. 2 × 2 × 2 × 2 × 2 = 32.

Solve for the exponent

2^n = 32. n = log(32) / log(2) = 5. 100^n = 10 gives 0.5.

Solve for the base

a^2 = 9 has two real answers, 3 and −3. a^3 = −8 has one real answer, −2.

e as the base

e^1 = 2.718281828459. e^2 ≈ 7.3890560989307. A negative exponent gives a reciprocal: e^(−1) ≈ 0.36787944117144.

Imaginary result

(−2)^0.5 is not real. The calculator returns Unable to solve! instead of a complex number.

Frequently asked questions

How do I use the exponent calculator?
Enter any two of the base a, the exponent n, and the result a^n. The calculator solves for the missing value. The default example is 2^5 = 32. Check Use e as base (or type e) to raise Euler's number to a power.
What is an exponent?
Exponentiation a^n multiplies the base a by itself n times when n is a positive integer. A negative exponent takes a reciprocal (a^(−n) = 1 / a^n). A decimal exponent is a root (a^0.5 is the square root of a).
Can I enter a fraction such as 1/3?
No. Type the decimal form instead — 0.5 for a square root, 0.333… for a cube root. The letter e is accepted as the base; other letters are not.
What happens with a negative base?
Integer powers work as usual ((−2)^3 = −8, (−2)^4 = 16). A fractional exponent on a negative base is imaginary, and this calculator does not compute complex numbers — those inputs return Unable to solve!
Why is 0^0 equal to 1?
Some contexts leave 0^0 undefined, but the exponent law a^n × a^0 = a^n only holds if a^0 = 1. This calculator follows that convention, matching 0^0 = 1.

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