Exponent Calculator

Compute a^b with live results, optional steps, a curve for y = aˣ, and reference power tables.

Quick examples

Base a

Positive, negative, and decimal bases are supported where defined in the reals.

Exponent b

Decimals supported (e.g. 0.5 for a square root, ~0.333 for a cube root).

Decimal places

Enter a base and exponent for an instant result, or tap an example.

What is an exponent?

An exponent tells you how many times to multiply a base by itself. We write a^b and say "a to the power b". For example, 2³ = 2 × 2 × 2 = 8. Exponents model repeated multiplication, growth, and are closely tied to logarithms (the inverse operation).

Rules of exponents

Product: a^m × aⁿ = a^m+n
Quotient: a^m / aⁿ = a^m−n (a ≠ 0)
Power of a power: (a^m)ⁿ = a^mn
Zero: a⁰ = 1 for a ≠ 0

Negative exponent explained

A negative exponent means take the reciprocal: a⁻ⁿ = 1 / aⁿ. Example: 10⁻² = 1/100 = 0.01.

Fractional exponent explained

A fractional exponent is a root: a^1/2 = √a, a^1/3 = ∛a, and in general a^p/q = (the q-th root of a)^p for a ≥ 0 in the reals.

Examples

2³ = 8
5² = 25
10⁻² = 0.01
4^(1/2) = 2
27^(1/3) = 3

Power tables (reference)

Quick reference for integer exponents from −2 through 8 (where defined).

Powers of 2

Exponent	2ⁿ	Value
-2	2^-2	0.25000
-1	2^-1	0.50000
0	2⁰	1
1	2¹	2
2	2²	4
3	2³	8
4	2⁴	16
5	2⁵	32
6	2⁶	64
7	2⁷	128
8	2⁸	256

Powers of 3

Exponent	3ⁿ	Value
-2	3^-2	0.11111
-1	3^-1	0.33333
0	3⁰	1
1	3¹	3
2	3²	9
3	3³	27
4	3⁴	81
5	3⁵	243
6	3⁶	729
7	3⁷	2187
8	3⁸	6561

Powers of 10

Exponent	10ⁿ	Value
-2	10^-2	0.010000
-1	10^-1	0.10000
0	10⁰	1
1	10¹	10
2	10²	100
3	10³	1000
4	10⁴	10000
5	10⁵	100000
6	10⁶	1000000
7	10⁷	10000000
8	10⁸	100000000

FAQs

What is 0 to the power of 0?: 0⁰ is not assigned a single standard value; in many contexts it is left undefined or treated specially. This calculator shows a message instead of a number.
Can the base be negative?: Yes for many integer exponents, but fractional powers of a negative base are not real numbers in general (they live in the complex plane). JavaScript’s Math.pow may return NaN for those cases.
How do I enter a square root?: Use exponent 0.5 (or enter 1/2 mentally as 0.5). For example, base 4 and exponent 0.5 gives 2.
Why does scientific notation appear?: Very large or very small magnitudes are easier to read in scientific notation; the main line still shows a fixed-decimal approximation when possible.