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Algebra & Functions

Exponent Calculator

Enter a base and an exponent. Whole exponents are shown as repeated multiplication, negative ones as reciprocals, and fractional ones as roots.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Try an example:

Answer1024

Step-by-step working 3 steps

1
Write it as a power
```
2^10
```
2
Repeated multiplication
2 is multiplied by itself 10 times.
3
Result
```
2^10 = 1024
```

How to use the exponent calculator

Enter the base.
Enter the exponent as a number or fraction.
Read the result and the method used.
Compare with the rules above.

Exponent rules

aᵐ · aⁿ = aᵐ⁺ⁿ
aᵐ / aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁻ⁿ = 1 / aⁿ
a^(p/q) = (q-th root of a)ᵖ
a⁰ = 1

0⁰ is undefined, and a negative base with a fractional exponent has no real value.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

2^10

Answer1024

Step-by-step working 3 steps

1
Write it as a power
```
2^10
```
2
Repeated multiplication
2 is multiplied by itself 10 times.
3
Result
```
2^10 = 1024
```

2^−3

Answer0.125

Step-by-step working 4 steps

1
Write it as a power
```
2^−3
```
2
Multiply the base 3 times
```
2 × 2 × 2 = 8
```
3
Negative exponent means reciprocal
```
2^−3 = 1 / 2^3 = 1 / 8
```
4
Result
```
2^−3 = 0.125
```

9^(1/2)

Answer3

Step-by-step working 3 steps

1
Write it as a power
```
9^(1/2)
```
2
Fractional exponent = root and power
```
9^(1/2) = (2th root of 9)^1
```
The denominator is the root, the numerator is the power.
3
Result
```
9^0.5 = 3
```

(−2)^3

Answer−8

Step-by-step working 3 steps

1
Write it as a power
```
−2^3
```
2
Multiply the base 3 times
```
(−2) × (−2) × (−2) = −8
```
3
Result
```
−2^3 = −8
```

Common mistakes to avoid

Reading −2² as 4

Without brackets the exponent applies first: −2² = −4. Use (−2)² for 4.

Multiplying base and exponent

2³ is 2 × 2 × 2 = 8, not 2 × 3 = 6.

Adding exponents when bases differ

aᵐ · bⁿ does not simplify by adding exponents unless the bases match.

Frequently asked questions

What does a negative exponent mean?

It means a reciprocal: 2⁻³ = 1/2³.

What is a fractional exponent?

A root: 9^(1/2) is the square root of 9.