Exponent Calculator
Any number to any power, whole, negative or fractional, with the working shown.
Good to know. Fold a sheet of paper 42 times and, on paper at least, it reaches the Moon. Powers of 2 grow fast.
How it works
In plain words
A whole power multiplies the base by itself that many times. A negative power is one divided by the positive power. A fractional power is a root: to the power ½ is the square root, ⅓ the cube root.
The formula
xⁿ = x × x × … × x (n times) x⁻ⁿ = 1 ÷ xⁿ x^(1/n) = ⁿ√x x⁰ = 1
Worked example
2 to the power 10 is ten 2s multiplied together: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024, or 1.024 × 10³.
Sources
No outside data or rates: this is plain arithmetic.
6 automated tests check its answers on every change.
About the exponent calculator
An exponent says how many times to multiply a number by itself. 2³ is 2 × 2 × 2 = 8, and 10⁶ is a million. Exponents are the language of things that grow or shrink by a constant factor: compound interest, populations, computer memory and the Richter scale.
The rules extend naturally beyond whole numbers. Anything to the power 0 is 1, because dividing x² by x² leaves 1. A negative exponent means one over the positive power: 2⁻³ = 1/8 = 0.125. A fractional exponent is a root: 9^0.5 is the square root of 9, 3, and 8^(1/3) is the cube root of 8, 2. Combined, 8^(2/3) is the cube root of 8, squared: 4.
Two traps catch people. A negative base with a fractional exponent, such as (−8)^0.5, has no real answer, and −2² usually means −(2²) = −4, not (−2)² = 4, so use brackets. And 0⁰ is defined as 1 by convention in most calculators, though mathematicians debate it.
Very large and very small results are shown in scientific notation as well. For roots on their own, use the square root calculator; for powers of ten, the scientific notation calculator.
Questions people ask
What is 2 to the power of 10?
1,024: ten 2s multiplied together.
What does a negative exponent mean?
One divided by the positive power: 5⁻² = 1 ÷ 25 = 0.04.
What is a number to the power of 0.5?
Its square root: 16^0.5 = 4.