Compute x raised to the power y with exact big-integer results, scientific notation and step-by-step expansion. Includes reverse modes to find the base or exponent.
xy = ?
Enter a valid number
Enter a valid number
Result
1024
Scientific1.024 × 103
Decimal1024
Expansion2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2
xy = r
Enter a valid number
Enter a non-zero number
Base x
2
Formulax = r1/y
Check210 = 1024
xy = r
Enter x > 0, x ≠ 1
Enter r > 0
Exponent y
10
Formulay = logx(r) = ln(r) / ln(x)
Check210 = 1024
Quick presets
Exponent rules
x⁰ = 1Any non-zero number raised to the zero power equals 1. By convention 0⁰ is also taken as 1.
x¹ = xA number raised to the first power is itself.
x⁻ⁿ = 1 / xⁿNegative exponent means the reciprocal of the positive power.
x^(1/n) = ⁿ√xA fractional exponent is an nth root. e.g. 16^(1/2) = √16 = 4.
xᵃ · xᵇ = xᵃ⁺ᵇMultiply same-base powers: add the exponents.
(xᵃ)ᵇ = xᵃᵇPower of a power: multiply the exponents.
Reference tables
Powers of 2
Powers of 10
Squares n²
FAQ
What does the exponent mean?
The exponent tells how many times the base is multiplied by itself. In 2⁵, the base 2 is used as a factor five times: 2·2·2·2·2 = 32.
Why is any number to the zero power 1?
Because xⁿ / xⁿ = 1, and by the quotient rule xⁿ / xⁿ = xⁿ⁻ⁿ = x⁰. So x⁰ must equal 1 for x ≠ 0. The case 0⁰ is a convention — most contexts use 0⁰ = 1.
What does a negative exponent mean?
A negative exponent is the reciprocal of the positive version: x⁻ⁿ = 1 / xⁿ. For example 2⁻³ = 1 / 2³ = 1/8 = 0.125.
How does a fractional exponent work?
A fractional exponent is a root. x^(1/n) = the n-th root of x, and x^(m/n) = the n-th root of x raised to the m-th power. So 16^(1/2) = √16 = 4, and 8^(2/3) = (∛8)² = 2² = 4.
Can the base be negative?
Yes for integer exponents: (−2)³ = −8, (−2)⁴ = 16. For fractional exponents with even denominator (like square roots) a negative base gives a non-real result, so this calculator returns an error in that case.
How large a result can be computed?
For integer base and non-negative integer exponent the calculator uses exact big-integer arithmetic — results can be hundreds of digits long. For other inputs it falls back to floating point and shows the answer in scientific notation when needed.
Copied
Raise any base to any exponent and see the result three ways: as a plain number, in scientific notation, and as a step-by-step expansion. For integer base and non-negative integer exponent the calculator uses big-integer arithmetic, so answers like 2^64 = 18446744073709551616 are exact. For fractional, negative and irrational exponents it falls back to floating point and shows enough precision for everyday work.nnThe calculator also handles two reverse modes. Enter a result and an exponent to find the base (x = r^(1/y)). Enter a base and a result to find the exponent (y = log_x r = ln r / ln x). Negative bases with non-integer exponents are flagged because the real-number answer does not exist.nnExample: 2^10 = 1024; 10^6 = 1,000,000; 2^-3 = 0.125; 16^(1/2) = 4. Reference tables cover powers of 2, powers of 10 and squares from 1 to 20.