The Exponent Calculator solves for any one of the base, exponent or result in the equation baseᵉˣᵖᵒⁿᵉⁿᵗ = result, including negative and fractional exponents and the constant e.
| 2^5 | 32 |
An exponent says how many times a base is multiplied by itself: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Exponents make very large and very small numbers easy to write and are the basis of compound interest, population growth, radioactive decay and scientific notation.
aᵐ × aⁿ = aᵐ⁺ⁿ. aᵐ ÷ aⁿ = aᵐ⁻ⁿ. (aᵐ)ⁿ = aᵐⁿ. (ab)ⁿ = aⁿbⁿ. a⁰ = 1 for a ≠ 0. a⁻ⁿ = 1 ÷ aⁿ. a^(1/n) = ⁿ√a, and a^(m/n) = (ⁿ√a)ᵐ.
If the result and base are known, the exponent is log(result) ÷ log(base): 2ˣ = 32 gives x = 5. If the exponent and result are known, the base is result^(1/exponent): x⁵ = 32 gives x = 2.
e ≈ 2.71828 is the base of natural logarithms. eˣ describes continuous growth, such as continuously compounded interest: $1 at 100% interest compounded continuously for a year grows to e dollars.
What is 0⁰? Usually defined as 1 in algebra, though it is indeterminate in calculus.
Can a negative base have a fractional exponent? Not in real numbers when the root is even.
What is a googol? 10¹⁰⁰.