What does a negative exponent mean?

It means "one divided by the positive power". 2^(−3) is 1/(2^3) = 1/8 = 0.125. A negative exponent inverts, it never makes the result negative.

What does a fractional exponent mean?

The denominator is a root and the numerator is a power. 8^(2/3) means the cube root of 8, squared: ∛8 = 2, then 2² = 4.

Why is anything to the power of zero equal to one?

Because x^n ÷ x^n = x^(n−n) = x^0, and anything divided by itself is 1. The only exception is 0^0, which is conventionally defined as 1 in combinatorics but left undefined in analysis.

Math

Exponent Calculator

Enter a base and an exponent to see the result.

The link carries your figures, so it reopens on exactly these numbers.

The formula

result = base ^ exponent

reciprocal = 1 ÷ result = base ^ (−exponent)

Worked example

Two to the tenth power

2^10 = 1,024
2^(−10) = 1/1,024 ≈ 0.000977

Where this goes wrong

A negative base with a fractional exponent

(−8)^(1/3) is −2 in algebra — the real cube root of −8. But most calculators evaluate it as e^((1/3) × ln(−8)), and since the logarithm of a negative number is complex, they return an error or NaN instead. This calculator returns the result when the exponent is a unit fraction with an odd denominator, and an error otherwise.

Questions

What does a negative exponent mean?: It means "one divided by the positive power". 2^(−3) is 1/(2^3) = 1/8 = 0.125. A negative exponent inverts, it never makes the result negative.
What does a fractional exponent mean?: The denominator is a root and the numerator is a power. 8^(2/3) means the cube root of 8, squared: ∛8 = 2, then 2² = 4.
Why is anything to the power of zero equal to one?: Because x^n ÷ x^n = x^(n−n) = x^0, and anything divided by itself is 1. The only exception is 0^0, which is conventionally defined as 1 in combinatorics but left undefined in analysis.