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Exponent Calculator

Calculate powers, negative and fractional exponents, and scientific notation with full step-by-step breakdowns.

Base

Exponent

2^?

Exponent rules

xᵃ · xᵇ = xᵃ⁺ᵇ · xᵃ / xᵇ = xᵃ⁻ᵇ · (xᵃ)ᵇ = xᵃᵇ · x⁻ⁿ = 1/xⁿ · x¹ᐟⁿ = ⁿ√x · x⁰ = 1

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Everyday Uses

Understanding growth

Doublings — of bacteria, followers, or rumors — are exponents in action. See how fast they explode.

Compound growth intuition

1.07²⁰ shows what 7% annual growth does over 20 years — the heart of investing math.

Tech numbers

Make sense of 2¹⁰ = 1,024 and why storage sizes come in the powers they do.

Verifying negative and fractional powers

Verify powers, negative exponents, and fractional exponents with exact results.

The folded paper claim

Fold a sheet 42 times and it would reach the Moon. The claim sounds absurd until you write it as 2⁴² — repeated doubling is far less intuitive than it feels.

Doubling times

Bacteria, compound interest and a share that keeps spreading all double on a fixed interval. Dividing 70 by the growth rate gives that doubling time in your head.

Frequently Asked Questions

How do you calculate an exponent (power)?

xⁿ means multiplying x by itself n times: x × x × x... (n times). Example: 2⁴ = 2 × 2 × 2 × 2 = 16. For large or non-integer exponents, calculators use logarithms internally: xⁿ = exp(n × ln(x)), which works for any real exponent as long as x > 0 (or x is negative with an integer exponent).

What does a negative exponent mean?

A negative exponent means "take the reciprocal": x⁻ⁿ = 1 / xⁿ. Example: 2⁻³ = 1/2³ = 1/8 = 0.125. This follows directly from the exponent division rule (xᵃ/xᵇ = xᵃ⁻ᵇ): since x⁰ = 1, dividing by xⁿ more times than you multiply produces a negative exponent and a fractional result.

What does a fractional exponent mean?

A fractional exponent represents a root: x^(1/n) = ⁿ√x. More generally, x^(m/n) = (ⁿ√x)ᵐ. Example: 8^(1/3) = ³√8 = 2 (the cube root of 8). 4^(3/2) = (√4)³ = 2³ = 8. Fractional exponents only produce a real result for negative bases when the denominator (root) is odd — even roots of negative numbers are complex.

Why does any non-zero number to the power of 0 equal 1?

This follows from the exponent division rule: xⁿ/xⁿ = xⁿ⁻ⁿ = x⁰. Since any non-zero number divided by itself equals 1, x⁰ must equal 1 for the rule to remain consistent. The case 0⁰ is a special, debated edge case — in most contexts (including this calculator) it is treated as undefined or 1 depending on convention.

How are very large or very small exponent results displayed?

When a result is extremely large (≥10¹⁵) or extremely small (<10⁻⁹ but non-zero), this calculator automatically switches to scientific notation (e.g. 1.234560e+18) for readability, since displaying dozens of digits would otherwise be impractical. Otherwise, results are shown as standard decimal numbers rounded to 12 significant figures.