Exponent Calculator
Raise a base to any power — positive, negative, or fractional — and see the repeated multiplication worked out.
Exponent Calculator — input your values
Learn more
Did you know?
The exponent calculator raises any base to any exponent, handling positive, negative, and fractional powers.
Recommendation
Any number (except 0) raised to the power 0 is 1 — a common trap in exams.
Also worth knowing
To square a number quickly, use the pattern (a + b)² = a² + 2ab + b² for mental arithmetic.
What does this math calculator do?
The exponent calculator raises any base to any exponent, handling positive, negative, and fractional powers. For positive whole-number exponents it expands the power into repeated multiplication and shows the running products at every step — exactly how exponents are introduced in class.
Negative and fractional exponents are handled by the rules a^(−n) = 1/a^n and a^(p/q) = (q-th root of a)^p, and the calculator always reports the base squared and cubed alongside, so you can spot patterns in powers quickly.
Formula and variables
Any non-zero base raised to the power 0 equals 1. 0^0 is undefined. A negative base with a fractional exponent has no real result.
| Symbol | Meaning |
|---|---|
| a | The base |
| n | The exponent (whole, negative, or fractional) |
| a^n | The result, a raised to the power n |
Worked example
A population of 500 bacteria triples every hour. How many are there after 4 hours?
- Population = 500 × 3^4.
- 3^4 = 3 × 3 × 3 × 3 = 81.
- 500 × 81 = 40,500.
Answer: There are 40,500 bacteria after 4 hours.
Tips and common mistakes
Tips
- Any number (except 0) raised to the power 0 is 1 — a common trap in exams.
- To square a number quickly, use the pattern (a + b)² = a² + 2ab + b² for mental arithmetic.
- Remember a^(−1) = 1/a: a negative exponent flips the base into the denominator.
- Fractional powers are roots: 9^(1/2) = 3 and 27^(1/3) = 3, so you can evaluate them without a calculator.
Common mistakes to avoid
- Treating a^0 as 0 instead of 1.
- Writing a negative base with a fractional exponent and expecting a real result — it produces no real number.
- Multiplying the base by the exponent (3 × 4 = 12) instead of raising it (3^4 = 81).
Exponent Calculator — frequently asked questions
What does an exponent mean?
It tells you how many times to multiply the base by itself. 3^4 means 3 × 3 × 3 × 3 = 81. The base is multiplied four times, not multiplied by four.
What happens with a negative exponent?
It gives the reciprocal of the positive power: 2^(−3) = 1 ÷ 2^3 = 1/8.
What does a fractional exponent mean?
A fractional exponent indicates a root: a^(1/2) is the square root, a^(1/3) is the cube root, and a^(p/q) is the q-th root raised to p.
Why is any number to the power 0 equal to 1?
Because a^n ÷ a^n = a^(n−n) = a^0, and a^n ÷ a^n = 1. So a^0 = 1 for every non-zero base.
Can I use this calculator for square and cube roots?
Yes — enter an exponent of 0.5 for a square root (16^0.5 = 4) or 1/3 for a cube root (27^(1/3) = 3).
How do exponents grow?
Exponentially. Every extra unit of the exponent multiplies the result by the base, so values can become enormous very quickly — 2^10 is already 1,024.
How this calculator works
Exponent Calculator uses the formula shown above (a^n = a × a × ... × a (n times) · a^(−n) = 1/a^n · a^(1/2) = √a) and computes the result instantly in your browser — no data leaves your device.