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Exponents & Powers Calculator

Calculate base raised to the power of exponent (x^y).

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Results

Power Value

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Assumptions

  • The base and exponent are finite real numbers.
  • The result follows standard real-number behavior from JavaScript's power function.
  • Some inputs, like 0^0 or negative fractional powers, are mathematically undefined or may return NaN.

Sensitivity preview

Base -10%: Power Value 5.83

Base Current: Power Value 8

Base +10%: Power Value 10.65

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About this Exponent Calculator

Exponents (or powers) represent repeated multiplication. Writing $2^5$ is much faster than writing $2 \times 2 \times 2 \times 2 \times 2$. This calculator handles basic powers as well as complex fractional and negative exponents.

Who this calculator is for

  • Students working on powers, radicals, and exponent rules.
  • Anyone modeling growth, decay, or scientific notation problems.
  • People who need a quick check for fractional or negative exponent results.

When to use it

  • Use this calculator to raise a base to a whole, negative, or decimal exponent.
  • Use it to compare exponent rules with roots and logarithms.
  • Use it for growth, decay, and scientific notation math.

How to use this calculator

  1. Enter the Base number.
  2. Enter the Exponent (power).
  3. The result is the base multiplied by itself 'exponent' times.

Key assumptions

  • The base and exponent are finite real numbers.
  • The result follows standard real-number behavior from JavaScript's power function.
  • Some inputs, like 0^0 or negative fractional powers, are mathematically undefined or may return NaN.

Accuracy and testing

Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.

View accuracy page

How this calculator works

* Positive Integer: $x^n = x \times x \dots$ (n times). * Negative Exponent: $x^{-n} = 1 / x^n$. * Fractional Exponent: $x^{1/n} = \sqrt[n]{x}$.

Inputs explained

Base

The number being multiplied.

Exponent

The power to which the base is raised. Can be positive, negative, or a decimal.

Understanding your results

Large exponents grow numbers very quickly (exponential growth). Negative exponents result in small fractions (decimals close to 0).

Example scenarios

Square

$5^2 = 25$.

Cube

$3^3 = 27$.

Negative Power

$2^{-2} = 1 / 2^2 = 1/4 = 0.25$.

Zero Power

$100^0 = 1$.

Key Features

  • High Precision
  • Negative Exponent Support
  • Decimal Power Support

Tips & Best Practices

  • Any non-zero number raised to the power of 0 is 1.
  • Scientific notation uses powers of 10 (e.g., $1.5 \times 10^6$) to express large numbers.
  • Fractional powers like $x^{0.5}$ are the same as square roots.

Glossary of Terms

Base
The number that gets multiplied when using an exponent.
Exponent
The superscript number indicating how many times to use the base in multiplication.
Squared
Raising a number to the power of 2.
Cubed
Raising a number to the power of 3.

Frequently Asked Questions

What is X to the power of 0?
Any non-zero number to the power of 0 is 1. (e.g., $5^0 = 1$).
What does a negative exponent mean?
A negative exponent represents the reciprocal. $x^{-n}$ is equal to $1 / x^n$. It effectively moves the number to the denominator.
How do fractional exponents work?
Fractional exponents represent roots. $x^{1/2}$ is the square root of $x$. $x^{1/3}$ is the cube root.