Exponent Calculator
Powers of any base, exact big powers, and solve for the exponent or base.
About this tool
Choose whether to calculate bⁿ, find the exponent n, or find the base b. Enter whole numbers, decimals or fractions such as 1/3. Whole-number powers of whole numbers are shown exactly, however many digits they have, with scientific notation for large results and a note explaining the rule used.
How exponents work
An exponent tells you how many times to multiply a number by itself: 2¹⁰ = 2 × 2 × … × 2 = 1,024. A few rules cover everything else. Any non-zero number to the power 0 is 1. A negative exponent is a reciprocal, so 2⁻³ = 1 ÷ 2³ = 0.125. A fractional exponent is a root: 8^(1/3) is the cube root of 8, which is 2, and 27^(2/3) = (cube root of 27)² = 9. When multiplying powers of the same base you add the exponents, and when dividing you subtract them. To find an unknown exponent, use logarithms: if 2ⁿ = 1,024, then n = log 1,024 ÷ log 2 = 10. To find an unknown base, take the root: if b³ = 27, then b = 27^(1/3) = 3. Powers grow fast: 2¹⁰⁰ has 31 digits, which ordinary calculators can only show approximately, so this tool uses exact integer arithmetic for whole-number powers. Honest limits: a negative base with a fractional exponent only has a real answer for odd roots, so (−8)^(1/3) = −2 but (−8)^(1/2) isn't a real number. 0⁰ is a matter of convention. The log calculator solves logarithms, the big number calculator handles huge integers and the scientific calculator covers the rest.
Frequently asked questions
What is a negative exponent?
A reciprocal: b⁻ⁿ = 1 ÷ bⁿ. For example, 10⁻² = 0.01.
What does a fractional exponent mean?
A root. b^(1/n) is the nth root of b, and b^(m/n) is that root raised to the power m.
Why is anything to the power 0 equal to 1?
Because bⁿ ÷ bⁿ = b⁰ and any non-zero number divided by itself is 1.
Is my data saved?
No. The calculation runs in your browser and nothing is stored or sent.