Exponent Calculator
Free exponent calculator: raise any base to any power, including negative and fractional exponents, with the expanded multiplication shown.
About the Exponent Calculator
An exponent tells you how many times to multiply a base by itself: bⁿ = b × b × … × b (n times). This free exponent calculator evaluates any power instantly — positive, negative, zero or fractional exponents — and for small whole-number powers writes out the expanded multiplication so students can see exactly what 2¹⁰ = 2 × 2 × … × 2 means.
It applies the standard rules: b⁰ = 1 for any non-zero base, b⁻ⁿ = 1 ÷ bⁿ, and b^(1/n) is the n-th root — so 8^(1/3) = 2. Very large or small results switch to scientific notation automatically, and impossible real-number cases (a negative base with a fractional exponent) are explained rather than shown as NaN. Handy for students from middle school through engineering, and anyone checking compound growth by hand.
How to Use the Exponent Calculator
- 1Enter the base number.
- 2Enter the exponent — negatives and fractions are allowed.
- 3Read the result, its reciprocal and the expanded multiplication for small integer powers.
Frequently Asked Questions
How do exponents work with an example?
2¹⁰ means multiplying 2 by itself ten times: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024. Each extra unit in the exponent multiplies the result by the base again, which is why powers grow so fast.
What does a negative exponent mean?
A negative exponent is a reciprocal: b⁻ⁿ = 1 ÷ bⁿ. So 2⁻³ = 1 ÷ 2³ = 1 ÷ 8 = 0.125. The sign of the exponent never makes the result negative — it moves the value below 1 instead.
What is a fractional exponent?
A fractional exponent is a root: b^(1/n) = ⁿ√b, and b^(m/n) = (ⁿ√b)^m. For example 8^(1/3) = ∛8 = 2, and 8^(2/3) = 2² = 4. This calculator evaluates them directly for any positive base.
Why does anything to the power 0 equal 1?
Dividing consecutive powers shows it: b³ ÷ b³ = b^(3−3) = b⁰, and any number divided by itself is 1. So 5⁰ = 1, 1000⁰ = 1. The one exception is 0⁰, which is undefined in most contexts (many calculators return 1 by convention).