PowerLab

Power Calculator

bⁿ — any base, any exponent.

Base b

Exponent n

bⁿ

1,024

bⁿ

What you entered

Base b: 2Exponent n: 10

1
Raise base to the exponent
2^10= 1024

Result

bⁿ: 1,024

2 raised to the power of 10 is 1,024.

Powers and exponents

The base raised to the exponent. Negative exponents give reciprocals and fractional exponents give roots.

Expression	Result	Note
2^8	256	A byte's worth of values
2^10	1024	One kibibyte
3^4	81	Whole-number power
5^3	125	Cube of 5
10^6	1000000	One million
2^-3	0.125	Same as 1 divided by 8
9^0.5	3	Same as the square root of 9

The last two rows are the ones that unlock the notation. A negative exponent means the reciprocal, so 2 to the -3 is 1 over 2 cubed, or 0.125. A fractional exponent means a root, so anything to the power 0.5 is its square root and to the power one third is its cube root. Any non-zero number to the power 0 is 1, which follows from the rule that dividing powers subtracts exponents. Powers of 2 dominate computing because each bit doubles the number of representable values - 2^10 being 1,024 is why a kilobyte was traditionally not 1,000 bytes.

Repeated multiplication, compressed

bⁿ means multiply b by itself n times — 2⁵ = 2×2×2×2×2 = 32. Negative exponents flip to a fraction (2⁻¹ = ½) and fractional exponents become roots (2^0.5 = √2).

Why exponents grow so fast

Because each increase in the exponent multiplies the result again rather than adding to it, powers grow exponentially — the basis for compound interest, population growth, and computing storage sizes.

Frequently asked questions

What does a negative exponent mean?

A negative exponent means 'one over' the positive power: 2⁻³ = 1/2³ = 1/8 = 0.125. In general, b⁻ⁿ = 1/bⁿ. It's the reciprocal — moving from the numerator to the denominator (or vice versa) flips the sign of the exponent.

What does a fractional exponent mean?

A fractional exponent combines powers and roots: b^(m/n) = ⁿ√(bᵐ). So 8^(2/3) = ∛(8²) = ∛64 = 4. The denominator is the root, the numerator is the power. b^(1/2) = √b, b^(1/3) = ∛b.

Why is anything to the power of 0 equal to 1?

The pattern: 2³=8, 2²=4, 2¹=2 — each time the exponent drops by 1, you divide by 2. So 2⁰ = 2÷2 = 1. This holds for any nonzero base. It also keeps the exponent rule bᵐ × bⁿ = bᵐ⁺ⁿ consistent: b³ × b⁰ = b³ requires b⁰ = 1.