Exponent Calculator

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

By Konstantin Iakovlev · Updated April 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 and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

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 you might project a 6.25% annual return on a $50,000 investment running ten years out to 2026, 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: Projecting 2026 Investment Growth with Fractional Exponents

  1. 1 Imagine you invested $10,000 at the beginning of 2024, expecting an average annual return of 7.5%. You want to know its value by mid-2026.
  2. 2 Here, the base is your initial investment plus the growth factor: 1 + 0.075 = 1.075. The power is the number of years: 2.5 (from beginning of 2024 to mid-2026). So, we need to calculate 10,000 * (1.075)^(2.5).
  3. 3 Using the calculator, (1.075)^(2.5) ≈ 1.1957. Therefore, 10,000 * 1.1957 = $11,957.00.
  4. 4 By mid-2026, your initial $10,000 investment, with a consistent 7.5% annual return, is projected to be worth approximately $11,957.00. This demonstrates the power of fractional exponents in calculating growth over partial periods.

Source: Khan Academy · Last updated: April 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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