Power & Root Calculator
Squares, cubes, nth powers, square roots and nth roots — all in one place.
TL;DR — Power & Root Calculator: A power and root calculator computes exponents (x raised to the power of y) and radicals (the nth root of x). Cal44 supports any real positive base and any real exponent, including fractional exponents (which represent roots).
What is the Power & Root Calculator?
A power and root calculator computes exponents (x raised to the power of y) and radicals (the nth root of x). Cal44 supports any real positive base and any real exponent, including fractional exponents (which represent roots).
How to use the Power & Root Calculator
- For powers: enter the base, then the exponent. Read x^y.
- For roots: enter the radicand (the number under the root), then the degree (2 for square, 3 for cube, etc.). Read the nth root.
- Fractional exponents act as roots: x^(1/3) = ∛x.
Formula
x^y is x multiplied by itself y times (when y is a positive integer). The nth root of x is the number r such that rⁿ = x. x^(1/n) = ⁿ√x
Negative bases are valid for integer exponents only. Fractional exponents of negative numbers are complex.
Worked example
2^10 = 1024. 5^0.5 = √5 ≈ 2.236. ∛125 = 5. 7^(1/4) ≈ 1.627.
Frequently asked questions
What is a power?
Repeated multiplication. 3^4 means 3 × 3 × 3 × 3 = 81.
What is a root?
The inverse of a power. The square root of 81 is 9 because 9² = 81.
Can I take the square root of a negative number?
Not in real numbers — that requires complex numbers (i). Cal44 returns an error for negative radicands with even-degree roots.
What is 0 to the power of 0?
Conventionally defined as 1 for most practical mathematics, though it's technically an indeterminate form in calculus.
How do fractional exponents work?
x^(p/q) = (ⁿ√x)^p — apply the qth root and then raise to the pth power (or vice versa). For example, 8^(2/3) = (∛8)² = 2² = 4.