Power and Root Calculator
This power and root calculator lets you work with exponents and radicals in a single tool. In power mode you raise any base to any exponent — whole numbers, decimals, and negative values are all supported, so you can compute anything from 2^10 to 5^-2 or 9^0.5. In root mode you extract the square root, cube root, or any nth root of a number. Each result is shown as a large figure alongside the exact expression that produced it, making it handy for homework, engineering, finance, and quick everyday math.
A power multiplies the base by itself as many times as the exponent indicates.
The nth root finds the number that, raised to the index, gives the radicand.
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Results are rounded to 6 decimals. Fractional exponents are equivalent to roots (for example, x^0.5 = √x).
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How it works
A power has the form base^exponent, meaning the base is multiplied by itself as many times as the exponent indicates: 2^3 = 2 × 2 × 2 = 8. A negative exponent gives the reciprocal, so 2^-3 = 1 / 2^3 = 0.125, and any nonzero base raised to 0 equals 1. A fractional exponent represents a root: x^(1/n) is the nth root of x, so 27^(1/3) = 3. The root mode uses this relationship directly: the nth root of a number is that number raised to the power 1/n. For a negative radicand the calculator returns a real result only when the index is odd (the cube root of -8 is -2); with an even index there is no real root, since no real number squared can be negative.
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Preguntas frecuentes
- What is a power?
- A power is a compact way of writing repeated multiplication. In the expression base^exponent, the base is the number being multiplied and the exponent tells you how many times. For example, 5^4 means 5 × 5 × 5 × 5 = 625. Powers appear everywhere, from area and volume formulas to compound interest and computer science.
- What does a negative exponent mean?
- A negative exponent means you take the reciprocal of the positive power. So x^-n = 1 / x^n. For example, 2^-3 = 1 / 2^3 = 1 / 8 = 0.125. The base cannot be zero, because dividing by zero is undefined. Any nonzero number raised to the power 0 equals 1.
- What is the difference between a square root and an nth root?
- A square root asks which number multiplied by itself gives the radicand, so √25 = 5 because 5 × 5 = 25. An nth root generalises this to any index: the cube root (index 3) of 27 is 3 because 3 × 3 × 3 = 27, and the fourth root of 16 is 2. A square root is simply an nth root with index 2.
- Why is there no real even root of a negative number?
- An even root (index 2, 4, 6, …) undoes an even power, and any real number raised to an even power is positive or zero — a negative times a negative is positive. So no real number can produce a negative result when raised to an even power, which means numbers like √-4 have no real value. Odd roots, such as the cube root, do work for negatives: the cube root of -8 is -2.
- How are fractional exponents related to roots?
- A fractional exponent is another way of writing a root. The expression x^(1/n) equals the nth root of x, so 16^(1/2) = 4 and 8^(1/3) = 2. More generally, x^(m/n) is the nth root of x raised to the power m. This is why entering 0.5 as an exponent in power mode gives you the square root.