How exponents work
An exponent tells you how many times to multiply the base by itself. A fractional exponent is a root — raising to the power ½ is the same as taking the square root.
- b — the base — the number being multiplied
- e — the exponent — how many times
More detail
Negative, zero, and fractional exponents
Any non-zero base to the power 0 is 1. A negative exponent is a reciprocal: b⁻ᵉ = 1 / bᵉ, so 2⁻³ = 1/8. A fractional exponent is a root: b^(1/2) = √b and b^(1/3) is the cube root. This is why the square-root output above equals raising the base to the power 0.5.
Powers of two. 2¹⁰ = 1024 ≈ 1000, which is why a kilobyte is 1024 bytes. Every 10 powers of two multiplies by roughly 1000: 2²⁰ ≈ a million, 2³⁰ ≈ a billion.
Frequently asked questions
What is 2 to the power of 10?
2¹⁰ = 1024 — two multiplied by itself ten times. Enter base 2 and exponent 10 above to confirm.
What is a fractional exponent like 2^0.5?
A fractional exponent is a root: 2^0.5 = √2 ≈ 1.41421. Raising to the power 1/3 gives the cube root, 1/4 the fourth root, and so on.
What does a negative exponent mean?
A negative exponent is the reciprocal of the positive one: b⁻ᵉ = 1 / bᵉ. For example 2⁻³ = 1 / 2³ = 1/8 = 0.125. Enter base 2, exponent −3 above to see it.
What is any number to the power of 0?
Any non-zero number raised to the power 0 equals 1 (for example 5⁰ = 1). 0⁰ is treated as 1 by this calculator's arithmetic, though it is a debated edge case in math.