Exponent Calculator

Calculate any base raised to any power including negative and fractional exponents.

By Konstantin Iakovlev · Updated September 2026 · Source: Khan Academy

Result

1,024.000000

Details

Standard Form1,024.000000
Expression2^10

Use the Exponent Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only. Results are estimates based on the information you provide and the assumptions described on this page.

How It Works

Raising a base to a power—positive, negative, or fractional—resolves to a single value here without the manual bookkeeping that invites mistakes. The reach is wide: in finance, (1 + r)^t compounds an annual return r over t years, while in the sciences the same operation describes exponential decay. Either way, the arithmetic that bogs people down gets handled in one step.

Everything traces back to the definition of exponentiation. A positive integer exponent 'n' means multiplying 'b' by itself 'n' times. A negative exponent flips that, so b^-n equals 1 / b^n. Fractional exponents b^(p/q) resolve to the q-th root of b raised to the p (that is, (q√b)^p), drawing on the standard identities so every exponent type lands correctly.

With fractional exponents, a zero denominator has no meaning, since dividing by zero is undefined. Order of operations also deserves attention once exponents sit alongside other terms. Negative bases trip people up most: (-8)^(1/3) comes out to -2, whereas (-8)^(2/3) is 4, not -4.

Example: Growth Over a Fractional Number of Years

  1. 1 $10,000 grows at an average of 7.5% a year, compounded annually. What is it worth after 2.5 years?
  2. 2 The growth factor per year is 1 + 0.075 = 1.075 and the time is 2.5 years, so the value is 10,000 × 1.075^2.5. Enter base 1.075 and exponent 2.5.
  3. 3 The calculator shows 1.198178. Multiplying: 10,000 × 1.198178 = $11,981.78.
  4. 4 The fractional exponent handles the half year: 1.075^2.5 = 1.075^2 × 1.075^0.5 = 1.155625 × 1.036822 = 1.198178, so the extra half year adds about 3.7% on top of two full years of growth.

Source: Khan Academy · Last updated: September 2026

Frequently Asked Questions

What does a negative exponent mean?
A negative exponent means the reciprocal. For example, 2^(-3) = 1/(2³) = 1/8 = 0.125. Move the base to the denominator and make the exponent positive.
What is a fractional exponent?
A fractional exponent combines a power and a root. For example, 8^(2/3) means the cube root of 8 squared: cube root of 64 = 4. The denominator is the root, the numerator is the power.
What is any number raised to the power of 0?
Any nonzero number raised to the power of 0 equals 1. For example, 5⁰ = 1, 100⁰ = 1, (-7)⁰ = 1. The only exception is 0⁰, which is undefined or defined as 1 by convention.

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