Enter a base, exponent, and root index.
Advanced Math Calculator
Power & Root Calculator
Calculate a base raised to an exponent and an nth root, including valid odd roots of negative numbers.
Instant answer
Formula breakdown
Browser-based
Mobile friendly
Interactive calculator
Enter your values
Use the example values or replace them with your own. Required validation happens before the calculation.
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Calculated answer
Result
Simple workflow
How to use the Power & Root Calculator
Follow these steps to get a reliable result and understand how it was produced.
The power uses bˣ.
The root uses b^(1/n) with real-domain checks.
Understanding the calculation
Powers repeatedly scale a base according to an exponent. Roots reverse integer powers, with domain restrictions for negative real inputs.
Power = bˣ; nth root = b^(1/n)The result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Exponential growth calculations
- Geometry and scientific formulas
- Checking squares, cubes, and roots
Accuracy tips
- A root index cannot be zero.
- Even roots of negative numbers are not real.
- Fractional exponents can represent roots.
Helpful answers
Power & Root Calculator FAQs
Important details about formulas, inputs, limitations, and result interpretation.
Can the exponent be negative?
Yes. A negative exponent gives the reciprocal of the corresponding positive power when the base is non-zero.
Can I take a cube root of a negative number?
Yes. Odd roots of negative numbers are real.
Why is an even root of a negative number rejected?
It has no real-number result.
What is a zero exponent?
Any non-zero base raised to zero equals 1.