Exponent Calculator
Root Calculator
About this calculator
Raise any base to any power, or take a root of a number. Type a base and an exponent for the first block, and a value and a root for the second. Results update as you type.
Exponents are repeated multiplication: 2¹⁰ means ten twos multiplied together, which is 1,024. A root undoes a power: the fourth root of 256 is 4 because 4⁴ is 256.
How to use it
- Enter the Base and the Exponent.
- For roots, enter the Value and the Root (n).
- Read the result beside each block.
Rules
bⁿ = b × b × … × b (n times). Useful rules: bᵐ × bⁿ = bᵐ⁺ⁿ, bᵐ ÷ bⁿ = bᵐ⁻ⁿ, (bᵐ)ⁿ = bᵐⁿ, b⁰ = 1, b⁻ⁿ = 1 ÷ bⁿ. The n-th root is x^(1/n).
Worked example
Examples
| 2¹⁰ | 1,024 |
| 5³ | 125 |
| 10⁻² | 0.01 |
| Fourth root of 256 | 4 |
| Square root of 144 | 12 |
Tips and common mistakes
- Anything to the power zero is 1.
- A negative exponent means a reciprocal: 2⁻³ = 1/8.
- Compound interest uses exponents: A = P(1 + r)ⁿ.
- Even roots of negative numbers are not real.
- Large powers grow very fast; results beyond about 10³⁰⁰ overflow.
Frequently asked questions
What is 2 to the power 10?
1,024.
What does a negative exponent mean?
The reciprocal of the positive power.
What is any number to the power 0?
1 (for non-zero numbers).
How do I find a root?
Raise the value to the power 1/n.
What is a fractional exponent?
It combines a power and a root: 8^(2/3) = 4.
Can the base be negative?
Yes, with whole-number exponents.