Exponent Calculator
Raise any base to any power — including negative, fractional, and decimal exponents. Ideal for compound interest, scientific calculations, and algebra.
About this calculator
Exponentiation is repeated multiplication: base^exp means the base is multiplied by itself exp times. The formula is result = base^exp (computed as Math.pow(base, exp)). Positive integer exponents are straightforward — 3^4 = 3 × 3 × 3 × 3 = 81. Negative exponents represent reciprocals: base^(−n) = 1 / base^n, so 2^(−3) = 1/8. Fractional exponents represent roots: base^(1/n) = the nth root of base, so 8^(1/3) = ∛8 = 2. Any base raised to the power of 0 equals 1 (by convention and mathematical consistency). Exponents appear in compound interest (A = P(1 + r)^t), population growth, physics, and computer science (binary powers like 2^10 = 1024).
How to use
Example 1 — Compound growth: A bacteria colony doubles every hour. After 6 hours, how large is a colony that started with 1 unit? Compute 2^6: enter Base = 2, Exponent = 6. Result = 64. Example 2 — Fractional exponent: What is 16^0.5? Enter Base = 16, Exponent = 0.5. Result = 4 (the square root of 16). Example 3 — Negative exponent: Enter Base = 5, Exponent = −2. Result = 5^(−2) = 1/25 = 0.04.
Frequently asked questions
What happens when you raise a number to a negative exponent?
A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent. The rule is: base^(−n) = 1 / base^n. For example, 4^(−2) = 1 / 4^2 = 1/16 = 0.0625. This rule ensures that the pattern of exponents remains consistent when extended below zero. Negative exponents appear frequently in scientific notation for very small numbers, such as 1 × 10^(−6) representing one millionth (0.000001).
How do fractional exponents relate to roots?
A fractional exponent of the form 1/n is equivalent to taking the nth root of the base: base^(1/n) = ∛ⁿbase. More generally, base^(m/n) = (ⁿ√base)^m — first take the nth root, then raise to the mth power. For example, 27^(2/3) = (∛27)^2 = 3^2 = 9. This connection unifies the concepts of roots and powers under a single notation system and is fundamental in algebra, calculus, and logarithms.
Why does any number raised to the power of zero equal one?
The rule base^0 = 1 follows directly from the laws of exponents. Consider that base^n / base^n = 1 for any non-zero base. Using the quotient rule for exponents, base^n / base^n = base^(n−n) = base^0. Therefore base^0 must equal 1. This holds for any non-zero base — 5^0 = 1, 1000^0 = 1, and (−7)^0 = 1. The expression 0^0 is mathematically indeterminate and is treated specially in different contexts.