Exponent calculator with steps

Enter a base and an exponent – negative, decimal or a fraction such as 2/3. You get the result, the exact value and every step of the working, including a check.

How it is calculated

How the exponent calculator works

A power aⁿ is shorthand for multiplying n equal factors: a is the base and n the exponent (or power). Example: 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024. For very large results the calculator also prints the exact value with every digit (2¹⁰⁰ has 31 digits) and the scientific notation (1.26765060023 × 10³⁰).

Exponent rules and special exponents

Rule	Formula	Example
Zero exponent	a⁰ = 1 (a ≠ 0)	7⁰ = 1
Negative exponent	a⁻ⁿ = 1 / aⁿ	2⁻³ = 1/8 = 0.125
Fractional exponent	a^(p/q) = (qth root of a)^p	8^(2/3) = (∛8)² = 2² = 4
Product rule	aᵐ · aⁿ = aᵐ⁺ⁿ	2³ · 2⁴ = 2⁷ = 128
Quotient rule	aᵐ / aⁿ = aᵐ⁻ⁿ	5⁶ / 5⁴ = 5² = 25
Power of a power	(aᵐ)ⁿ = aᵐ·ⁿ	(3²)³ = 3⁶ = 729
Negative base	even exponent → positive, odd → negative	(−2)⁴ = 16, (−2)³ = −8

Watch the notation: −2⁴ means −(2⁴) = −16; only (−2)⁴ equals 16. This calculator always raises the base you type as a whole, so −2 to the 4th is (−2)⁴ = 16.

nth roots

The nth root ⁿ√x undoes a power: it is the number that, multiplied by itself n times, gives x. In exponent form ⁿ√x = x^(1/n). Example: ∛27 = 3 because 3³ = 27 (the check). Roots that do not come out even are simplified: √72 = √(36 × 2) = 6√2 ≈ 8.485.

Roots of negative numbers: odd roots have a real answer, ∛(−8) = −2 since (−2)³ = −8. Even roots such as √−4 are not real numbers (the complex answer is 2i).

Logarithms: log, ln and change of base

A logarithm answers “b to what power gives x?”: log_b x = y means b^y = x. So log₂ 8 = 3 because 2³ = 8. ln is the natural log with base e ≈ 2.71828, log on most calculators is the common log with base 10, and log₂ (lb) is the binary log used in computing. Any other base follows from the change-of-base formula:

log_b x = ln x / ln b – example: log₃ 10 = ln 10 / ln 3 = 2.302585 / 1.098612 ≈ 2.0959.

Logarithms exist only for x > 0, and the base must be positive and not 1. If x is between 0 and 1 (with a base above 1), the result is negative: log₁₀ 0.01 = −2.

Special cases

0⁰ is indeterminate in calculus; algebra, combinatorics and calculators use 0⁰ = 1. The calculator shows 1 with a note.
0 to a negative power (0⁻¹ = 1/0) is undefined – division by zero.
Huge or tiny values beyond 10³⁰⁸ are computed via logarithms: 2⁵⁰⁰⁰ ≈ 1.41 × 10¹⁵⁰⁵.

Frequently asked questions

How do you calculate an exponent?

Multiply the base by itself as many times as the exponent says: 3⁴ = 3 × 3 × 3 × 3 = 81. For large exponents use the calculator – it also returns the exact integer with all digits.

What does a negative exponent mean?

A negative exponent means the reciprocal: a⁻ⁿ = 1/aⁿ. Example: 10⁻³ = 1/10³ = 1/1,000 = 0.001. The result gets smaller but never negative (for a positive base).

How do fractional exponents work?

The denominator is the root, the numerator the power: a^(p/q) = (qth root of a)^p. Example: 27^(2/3) = (∛27)² = 3² = 9. Just type the exponent as a fraction, e.g. 2/3.

How do I find a cube root?

Choose “nth root”, enter the radicand and index 3 – or use the power mode with exponent 1/3: ∛64 = 64^(1/3) = 4. Negative numbers work too: ∛(−64) = −4.

How do I calculate a log with any base?

Use the change-of-base formula: log_b x = ln x / ln b (or log x / log b). Example: log₅ 125 = ln 125 / ln 5 = 3. In the calculator just enter the number and the base; ln, log₁₀ and log₂ are always shown as well.

What is the difference between ln and log?

ln is the natural logarithm with base e ≈ 2.71828; log on a calculator usually means base 10. ln 10 ≈ 2.3026 while log 10 = 1. Conversion: ln x = log₁₀ x × ln 10.

What is 0 to the power of 0?

0⁰ is indeterminate in calculus, because the rules “a⁰ = 1” and “0ⁿ = 0” conflict. In algebra, combinatorics and on calculators the convention 0⁰ = 1 is used.

Sources and legal basis

As of: 27 September 2026