Instantly calculate powers (xⁿ) and roots (square, cube or any order), including negative and fractional exponents.
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For a square root use index 2; for a cube root, index 3.
2^10 = 1,024
2^10 = 1,024Standard mathematical formulas. Instant in-browser calculation, no account. Exact results for the values you enter.
A power multiplies the base by itself as many times as the exponent says. A root is the inverse operation — the nth root is the power 1/n:
2¹⁰ = 1024. √144 = 12 (index 2). ∛27 = 3 (index 3). With a negative exponent: 2⁻³ = 1 ÷ 8 = 0.125.
Multiply the base x by itself n times. For example, 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
Choose the “Root” mode with index 2. The square root of 144 is 12, because 12² = 144.
Use the “Root” mode with index 3. The cube root of 27 is 3, because 3³ = 27.
A negative exponent means the reciprocal: x⁻ⁿ = 1 ÷ xⁿ. For example, 2⁻³ = 1 ÷ 8 = 0.125.
A fractional exponent is a root: x^(1/2) = √x, and x^(1/3) = ∛x. For example, 9^(1/2) = 3.
Any non-zero number raised to the power 0 equals 1. For example, 7⁰ = 1.
Only for odd indices (cube root etc.): ∛(−8) = −2. The square root of a negative number has no real solution.
They are inverse operations: raising to a power (xⁿ) and taking the root (ⁿ√x) cancel each other. An nth root is the power 1/n.