Power and root calculator
Calculate powers (base raised to an exponent) and roots (square and nth).
Even-index roots require a non-negative base.
How the calculation works
A power base^exponent multiplies the base by itself "exponent" times: 2^4 = 2 × 2 × 2 × 2 = 16.
A root is the inverse: "what number to the nth power gives this?". The nth root is a fractional-exponent power: ⁿ√base = base^(1/n).
Step-by-step example
- Power: 5³ = 125
- Root: √49 = 49^(1/2) = 7
- Cube root: ³√27 = 3
Handy rules
- A negative exponent inverts: 2⁻³ = 1/8.
- Multiplying same-base powers adds exponents: 2³ × 2² = 2⁵.
- Any number (≠ 0) to the power 0 is 1.
Examples
- 10⁶ = 1,000,000; √144 = 12.
- 2⁻² = 1/4 = 0.25.
Frequently asked questions
What is a number to the power of zero?
Any number (except 0) raised to 0 equals 1.
What does a negative exponent mean?
It is the reciprocal of the positive power: base⁻ⁿ = 1 ÷ baseⁿ. E.g. 5⁻² = 1/25.
Can I take a root of a negative number?
An even (square) root of a negative has no real value (needs complex numbers). A cube root does: ³√−8 = −2.
Related calculators
More Students calculators
See all →LCM & GCD
Calculate the least common multiple (LCM) and greatest common divisor (GCD) of two numbers.
Grade needed
Find out the grade you need on the final exam to reach the required average.
Grade calculator
Find the percentage and letter grade of a test from the total questions and how many you missed.
Linear equation
Solve first-degree equations in the form ax + b = c, with a check of the result.
Fraction
Add, subtract, multiply and divide fractions, with the result already simplified.
GPA
Calculate your GPA on the 4.0 scale from letter grades and credit hours per course.
Weighted average
Calculate the weighted average from values and their corresponding weights.
Updated on June 18, 2026 · by Rafael Rossi · Methodology & sources