Toolstia / Exponent and root calculator
Exponent and root calculator
Work out x to the power of y, or the nth root of x, in one page. Whole-number powers are computed exactly, so 2 to the power of 100 shows every digit. Square roots are also simplified, so √72 shows as 6√2.
Power: x to the power of y
Root: the nth root of x
How it works
- Type a base and an exponent for a power.
- Or type a number and a root such as 2 for a square root or 3 for a cube root.
- Read the result, the exact digits and the simplified radical.
Exact powers
When the base and the exponent are whole numbers, the result is computed with big-integer arithmetic, so there is no rounding at all.
Roots
The nth root of x is x raised to the power 1/n. Odd roots of negative numbers are real (the cube root of −27 is −3). Even roots of negative numbers are shown as complex numbers.
Simplified radicals
The tool pulls perfect squares out of a square root, so √50 becomes 5√2.
Limits
Powers that overflow ordinary numbers are shown in scientific form. The exact digit display is capped at 3,000 digits.
Questions
Why can a negative base not take a fractional power?
The result is not a real number, so the tool tells you instead of guessing.
Can the exponent be negative?
Yes. A negative exponent gives the reciprocal, so 2 to the power of −2 is 0.25.
Is anything uploaded?
No. Your input stays in your browser and is never sent anywhere.