// compute xⁿ, roots, and exponents instantly
Calculate powers, exponents, square roots, and nth roots instantly. Compute xⁿ with precision — supports negative bases, decimal exponents, and large numbers.
Ready to calculate
Enter values and click CalculateSelect Power (xⁿ), Square Root (√x), or Nth Root (ⁿ√x) using the tabs at the top.
Type your base number and exponent (or root degree). Use quick presets for common calculations.
Click Calculate to see the result, scientific notation, and a step-by-step breakdown.
The Power & Exponent Calculator computes any base raised to any exponent (xⁿ), square roots, and arbitrary nth roots. It handles negative bases, decimal exponents, fractional powers, and displays results in both standard and scientific notation with a clear step-by-step breakdown.
xⁿ means multiplying x by itself n times. For example, 2³ = 2 × 2 × 2 = 8. The base is x, and the exponent is n. This calculator supports any real number base and exponent.
Yes. A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. For example, 2⁻³ = 1/8 = 0.125. The calculator handles negative exponents and shows the step-by-step reciprocal calculation.
The nth root of x (written ⁿ√x) is the number that, when raised to the power n, gives x. The cube root (³√x) is the most common: ³√27 = 3, because 3³ = 27. This tool calculates any nth root.
Yes. Decimal exponents are fully supported. For example, 4^0.5 = √4 = 2, and 8^(1/3) = ∛8 = 2. Enter the decimal value directly in the exponent field.
In the real number system, square roots of negative numbers are undefined (they produce imaginary numbers). This calculator operates in real numbers only. The even root of a negative number is similarly undefined here.
Scientific notation expresses very large or very small numbers as a mantissa times a power of 10 (e.g., 1.024 × 10³). It's commonly used in science and engineering to handle numbers like 2³² = 4,294,967,296 ≈ 4.29 × 10⁹.
The Power & Exponent Calculator is a free, browser-based tool for computing exponential expressions instantly. Whether you need to raise a number to a power, find a square root, or calculate an arbitrary nth root, this tool delivers precise results with a step-by-step breakdown — no sign-up, no server upload, and no installation required.
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Exponentiation is a mathematical operation where a base number (x) is multiplied by itself a specified number of times determined by the exponent (n). Written as xⁿ, the result is called the power. For example:
Exponentiation is fundamental in mathematics, computer science, physics, finance, and engineering. It underlies compound interest calculations, binary number systems, polynomial equations, and exponential growth models.
The square root of a number x (written √x) is the value that, when multiplied by itself, gives x. It's the inverse of squaring a number: √(x²) = x. For positive numbers, square roots are always real and positive. Common square roots include √4 = 2, √9 = 3, √16 = 4, and √25 = 5.
Irrational square roots — like √2 ≈ 1.41421 or √3 ≈ 1.73205 — cannot be expressed as simple fractions. Our calculator displays these to high precision, so you can use them confidently in equations and computations.
An nth root generalizes the square root concept. The nth root of x (ⁿ√x) is the number that, when raised to the power n, produces x. Key examples:
Nth roots are frequently used in compound interest formulas (where you need the nth root of a growth factor), in statistics (geometric mean calculation), and in signal processing.
This calculator handles several special and edge cases that simpler tools miss:
When computing powers like 2³² = 4,294,967,296 or 10¹⁵, results can become unwieldy to read. Scientific notation expresses these values compactly as a coefficient times a power of 10. Our calculator automatically generates the scientific notation equivalent alongside the full result, making it easy to verify magnitudes at a glance.
Software developers and system architects frequently rely on powers of 2 to understand memory, storage, and binary limits:
Use the quick preset buttons to jump straight to common developer calculations like 2¹⁰ or 2³².
Standard calculator apps often lack the ability to compute arbitrary nth roots, handle negative exponents clearly, or display step-by-step working. This tool bridges that gap — it's especially useful for students checking homework, developers verifying binary limits, scientists performing quick magnitude checks, and anyone who needs a reliable, instant exponent calculation without pulling out a scientific calculator.