Exponent Calculator
An exponent (or power) represents repeated multiplication of a base number by itself. The expression b^e means the base b multiplied by itself e times. This calculator evaluates any base raised to any exponent — including negative exponents, which produce reciprocals, and fractional exponents, which correspond to roots.
Exponents are fundamental in science, engineering, finance, and everyday mathematics. Negative exponents such as 2^(-3) = 1/8 are common in scientific notation and physics, while fractional exponents like 8^(1/3) = 2 are equivalent to nth roots. This tool handles all these cases and shows an expanded multiplication note for small integer exponents so you can verify the result step by step.
How it works
b^e = b × b × … × b (e times) for positive integer e. For negative e: b^(-e) = 1 / b^e. For fractional e = p/q: b^(p/q) = the q-th root of b^p. Computed via Math.pow(b, e) for full precision.
Use cases
- Computing compound interest growth (principal × rate^years)
- Converting between scientific notation and standard form
- Calculating areas and volumes using squared or cubed measurements
- Evaluating nth roots via fractional exponents (e.g., 27^(1/3) = 3)
- Solving exponential decay problems in physics and chemistry
Frequently asked questions
What does a negative exponent mean?
A negative exponent produces the reciprocal of the positive power: b^(−e) = 1 / b^e. For example, 2^(−3) = 1 / 2³ = 1/8 = 0.125. Negative exponents are common in scientific notation, where 10^(−6) represents one millionth.
What is any number raised to the power of 0?
Any nonzero number raised to the power of 0 equals 1, so 5^0 = 1 and (−273)^0 = 1. This follows from the quotient rule: b^n ÷ b^n = b^(n−n) = b^0, and any number divided by itself is 1. The expression 0^0 is conventionally treated as 1 in most calculators and programming languages, including this one.
How do fractional exponents work?
A fractional exponent p/q means taking the q-th root of the base raised to the p-th power: b^(p/q) = the q-th root of b^p. For example, 8^(1/3) = ∛8 = 2, and 27^(2/3) = (∛27)² = 3² = 9. This makes roots and powers part of the same unified notation.
What is 2 to the power of 10?
2^10 = 1,024, which is 2 multiplied by itself ten times. This value appears throughout computing: 1 kibibyte is 1,024 bytes, and successive powers of 2 (2, 4, 8, 16, …) underpin binary arithmetic. Enter base 2 and exponent 10 in the calculator to see the expanded multiplication note.
How do you calculate a negative fractional exponent like 4^(−1/2)?
Combine both rules: the negative sign takes the reciprocal and the fraction takes the root. So 4^(−1/2) = 1 / 4^(1/2) = 1 / √4 = 1/2 = 0.5. Note that fractional exponents of negative bases (such as (−8)^(1/2)) are not real numbers, so the calculator cannot return a real result for them.