About the Exponent Calculator
This exponent calculator works out bⁿ — a base raised to a power — for whole-number, negative, decimal and fractional exponents. Type an exponent like 10, −2, 0.5 or 2/3 and you get the exact result, the value in scientific notation and a written-out expansion so you can see what the power means.
Negative exponents give reciprocals (5⁻² = 1/25), fractional exponents give roots (27^(2/3) is the cube root of 27, squared, which is 9), and negative bases with odd roots stay real, so (−8)^(1/3) = −2. When there is no real answer, such as the square root of a negative number, the calculator says so instead of returning an error.
Use it for algebra homework, scientific notation, compound growth factors like 1.05³⁰, computing powers of two for storage sizes, or checking a calculator result. The chart shows how the power grows (or shrinks) step by step from b⁰ = 1.
With the default inputs, the result bⁿ is 1,024. Change any value above to recalculate instantly.
How to use the exponent calculator
- 1Enter the base number.
- 2Enter the exponent — a whole number, a decimal, a negative number or a fraction like 2/3.
- 3Read the result and its scientific notation.
- 4Check the expanded form to see how the power is built up.
Formula and method
For a positive whole-number exponent, bⁿ multiplies the base by itself n times. The laws of exponents extend this: b⁰ = 1, a negative exponent means the reciprocal (b⁻ⁿ = 1/bⁿ), and a fractional exponent p/q means take the qth root and raise it to the power p.
Decimal exponents are computed as e^(n·ln b), which is how scientific calculators evaluate them. For a negative base, a real answer exists only when the exponent is a whole number or a fraction with an odd denominator (like 1/3 or 2/5); otherwise the result is a complex number and is reported as not real.
- b
- Base — the number being multiplied
- n
- Exponent (power) — how many times, or a fraction for roots
- p/q
- Fractional exponent: q is the root, p the power
Worked examples
2 to the power of 10
Multiplying 2 by itself ten times gives 1,024 — the number of bytes in a kibibyte. Its reciprocal 2⁻¹⁰ is 0.0009765625.
Negative exponent: 5⁻²
5⁻² = 1/5² = 1/25 = 0.04. A negative exponent always means one over the positive power.
Fractional exponent: 27^(2/3)
The cube root of 27 is 3, and 3 squared is 9, so 27^(2/3) = 9.
Cube root of a negative: (−8)^(1/3)
Because (−2)³ = −8 and the root is odd, the real cube root of −8 is −2.
Growth factor 1.05³⁰
Growing 5% a year for 30 years multiplies a value by 1.05³⁰ ≈ 4.32 — the core of compound interest.
Frequently asked questions
How do you calculate exponents?+
Multiply the base by itself as many times as the exponent says: 3⁴ = 3 × 3 × 3 × 3 = 81. For negative, decimal or fractional exponents use the exponent laws or a calculator like this one.
What does a negative exponent mean?+
A negative exponent means the reciprocal of the positive power: b⁻ⁿ = 1/bⁿ. So 10⁻³ = 1/1000 = 0.001 and 2⁻¹ = 0.5.
What is a number to the power of 0?+
Any non-zero number raised to the power 0 equals 1, because bⁿ ÷ bⁿ = b⁰ = 1. The expression 0⁰ is usually defined as 1 in algebra and combinatorics.
What does a fractional exponent mean?+
A fractional exponent p/q means the qth root raised to the power p. For example 16^(1/2) = √16 = 4, 8^(1/3) = 2, and 32^(3/5) = 2³ = 8.
What are the main laws of exponents?+
bᵐ × bⁿ = bᵐ⁺ⁿ, bᵐ ÷ bⁿ = bᵐ⁻ⁿ, (bᵐ)ⁿ = bᵐⁿ, (ab)ⁿ = aⁿbⁿ, b⁰ = 1 and b⁻ⁿ = 1/bⁿ. They let you simplify expressions before calculating.