Exponents & Roots
Calculate powers and roots with growth visualizations
About this calculator
The Exponents & Roots Calculator handles powers and nth roots for any real number. Switch between power mode (base^exponent) and root mode (ⁿ√x) to compute results instantly with a growth visualization. Covers everything from simple squaring to cube roots and fractional exponents.
How to calculate powers and roots
- Pick power mode (base^exp) or root mode (ⁿ√x).
- Enter the base (or radicand) and the exponent (or root index).
- Read the result and the growth visualization.
- Switch modes to invert the operation and verify the answer.
Common examples
- 2^10 = 1,024
- 5^3 = 125
- √144 = 12 (square root, index 2)
- ∛27 = 3 (cube root, index 3)
- 2^0.5 = √2 ≈ 1.4142
Frequently asked questions
What is the difference between an exponent and a root?
An exponent (or power) repeats multiplication: 2^3 means 2 × 2 × 2 = 8. A root is the inverse: the cube root of 8 is 2, because 2 cubed equals 8. The calculator covers both directions.
Why is 0^0 indeterminate?
0^0 has two competing conventions: any nonzero number to the 0 power is 1, but 0 to any positive power is 0. There is no single agreed real-number answer, so the calculator shows an indeterminate state.
Can the base be negative?
In power mode, a negative base is allowed only when the exponent is an integer, so the result stays a real number. In root mode, negative radicands are allowed only when the root index is an odd integer, like the cube root of −8 = −2.
Why no complex results?
Version 1 stays in real numbers to keep the visualizations meaningful. Inputs that would force a complex answer (such as the square root of a negative number) show an explanatory message instead.