Exponent calculator with steps

Exponent calculator: 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.

Source: DLMF §4.2, NIST Digital Library of Mathematical Functions, ch. 4: logarithm, exponential, powers. Updated: 27 September 2026.

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).

How to calculate an exponent

Under “What do you want to calculate?” pick power, nth root or logarithm.
Enter base a and exponent n – for a root the radicand x and the index n, for a logarithm the number x and base b.
Read the result, the exact value, the scientific notation and the step-by-step solution with a check.

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.

Related tools: write very large or small results with the scientific notation converter, simplify fractions with the fraction calculator, and see powers of two in binary with the number base converter.

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 · Editorial policy

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