Exponent Calculator (Powers)
Calculate any power: whole, negative or fractional exponents, positive or negative bases. The result includes the scientific-notation form for very large or small answers, plus the exponent rules you need to work these by hand.
How to use this calculator
- Enter the base — the number being multiplied by itself.
- Enter the exponent — how many times. Negatives and decimals are allowed.
- Press Calculate. Very large or small results are also shown in scientific notation.
Formula used
Key rules: multiplying powers of the same base adds exponents (x² · x³ = x⁵); dividing subtracts them; a power of a power multiplies them ((x²)³ = x⁶). Anything (except 0) to the power 0 equals 1.
Example calculation
2¹⁰ = 1,024 — doubling ten times, the reason a kilobyte is 1,024 bytes.
2⁻³ = 1/2³ = 0.125, and 9^(1/2) = √9 = 3: negative exponents mean reciprocals, fractional exponents mean roots.
How exponents work
An exponent counts repeated multiplication: 2¹⁰ means multiplying ten 2s together. This compact notation is what makes exponential growth deceptive — each step multiplies rather than adds, so values explode: 2¹⁰ is about a thousand, 2²⁰ about a million, 2³⁰ about a billion.
The extensions are consistent, not arbitrary: negative exponents give reciprocals (so the dividing rule keeps working), fractional exponents give roots (so the multiplying rule keeps working), and x⁰ = 1 (so dividing xⁿ by itself works). Exponents power compound interest, population growth, radioactive decay and computer science alike.
Why use this calculator?
- Handle negative and fractional exponents, where mental arithmetic usually breaks down.
- See the reasoning rows explaining what a reciprocal or root exponent actually did.
- Get scientific notation automatically for astronomically large or small results.
Frequently asked questions
What does a negative exponent mean?
Take the reciprocal of the positive power: x⁻ⁿ = 1/xⁿ. So 5⁻² = 1/25 = 0.04. The negative flips the number below the fraction line; it never makes the result negative.
What does a fractional exponent like x^(1/2) mean?
A root: x^(1/2) is the square root, x^(1/3) the cube root, and x^(m/n) is the n-th root of xᵐ. So 8^(2/3) = (∛8)² = 2² = 4.
Why does anything to the power 0 equal 1?
Follow the pattern of dividing: 2³=8, 2²=4, 2¹=2 — each step divides by 2, so 2⁰ = 1. Formally, xⁿ ÷ xⁿ = x⁰ and anything divided by itself is 1. (0⁰ is the exception and is left undefined or set to 1 by convention.)