Exponent Calculator
An exponent tells you how many times to multiply a base by itself: 2¹⁰ means ten 2s multiplied, which is 1,024. Negative exponents give reciprocals and fractional exponents give roots. This calculator handles all three and also shows the answer in scientific notation.
How to use the exponent calculator
- Enter the base and the exponent. Decimals and negatives are allowed.
- Read the value of base^exponent, its scientific notation and reciprocal.
- Try 0.5 as the exponent to see square roots: 9^0.5 = 3.
Formula
- an = a × a × … × a (n times)
- a−n = 1 ÷ an
- a1/n = the n-th root of a
- am × an = am+n and (am)n = amn
- a0 = 1 for any a ≠ 0
Worked examples
Positive power
2^10 = 1,024. Doubling ten times is why computer memory comes in sizes like 1,024.
Fractional power
9^0.5 is the square root of 9, which is 3. And 8^(1/3) = 2 because 2 × 2 × 2 = 8.
The laws of exponents
| Rule | Example |
|---|---|
| Product: aᵐ × aⁿ = aᵐ⁺ⁿ | 2³ × 2⁴ = 2⁷ = 128 |
| Quotient: aᵐ ÷ aⁿ = aᵐ⁻ⁿ | 5⁶ ÷ 5⁴ = 5² = 25 |
| Power of a power: (aᵐ)ⁿ = aᵐⁿ | (3²)³ = 3⁶ = 729 |
| Zero: a⁰ = 1 | 7⁰ = 1 |
| Negative: a⁻ⁿ = 1/aⁿ | 10⁻² = 0.01 |
| Fractional: a^(1/n) = ⁿ√a | 27^(1/3) = 3 |
Why exponents grow so fast
Exponential growth doubles, triples or multiplies by a fixed factor each step. A sheet of paper folded 42 times would reach the Moon, because 2⁴² multiplied by the paper thickness is about 440,000 km. This is also why compound interest and viral spread feel slow at first and then explode.
Common squares and cubes
Knowing 1² to 15² (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225) and 1³ to 10³ (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000) speeds up mental arithmetic and helps you spot perfect squares in factoring problems.
Order of operations
Exponents come before multiplication, division, addition and subtraction. So 2 + 3² = 11, not 25, and −3² = −9. Use brackets when you mean (−3)².
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- Calculate 7^4.
Show answer
7^4: 2,401
- Calculate 5^-3.
Show answer
5^-3: 0.008
- Calculate 64^(1/3).
Show answer
64^0.3333333333: 4
Common mistakes to avoid
- Reading −3² as 9. It is −(3²) = −9; use (−3)² for 9.
- Thinking a⁰ = 0. Any non-zero number to the power 0 is 1.
- Taking an even root of a negative number, which has no real result.
Frequently asked questions
What is a negative exponent?
It means take the reciprocal: 2⁻³ = 1/2³ = 1/8.
What is 0 to the power of 0?
It is treated as undefined or 1 depending on context; most calculators show 1.
How do I multiply numbers with exponents?
If the bases match, add the exponents: 3² × 3⁴ = 3⁶.
Why can a huge power be inexact?
Computers store about 15–17 significant digits, so very large results are rounded.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.