Exponent Calculator

What Is an Exponent?

An exponent tells you how many times to multiply a number by itself. In aⁿ, the base a is the number being multiplied and the exponent n is the count, so 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Exponents are also called powers: "2 to the power of 5." They give a compact way to write very large and very small numbers, and they describe anything that grows or decays by a constant factor — compound interest, populations, radioactive decay and computer storage among them. This exponent calculator raises any base to any power and shows the answer instantly.

The Laws of Exponents

• Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ — same base, add the exponents.
• Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ — same base, subtract the exponents.
• Power of a power: (aᵐ)ⁿ = aᵐⁿ — multiply the exponents.
• Power of a product: (ab)ⁿ = aⁿbⁿ, and likewise (a/b)ⁿ = aⁿ/bⁿ.
• Zero exponent: a⁰ = 1 for any non-zero a.
• First power: a¹ = a.
• Negative exponent: a⁻ⁿ = 1/aⁿ — flip the base and make the exponent positive.

Fractional Exponents Are Roots

An exponent of 1/n means the nth root: 9^(1/2) = √9 = 3 and 27^(1/3) = 3. A fraction such as 8^(2/3) combines both ideas — take the cube root first (2), then square it (4). When you enter a fractional exponent here, write it as a decimal (for example 0.5 instead of 1/2).

Negative Bases

A negative base raised to a whole-number exponent has the same size as the positive version, but its sign depends on the exponent: even exponents give a positive result ((−2)⁴ = 16) and odd exponents give a negative one ((−2)³ = −8). Raising a negative number to a fractional power can lead to imaginary numbers, which a basic calculator will not return.

Why 0⁰ Is Debated

Most of algebra treats a⁰ as 1, and for convenience 0⁰ is often defined as 1 too, though some textbooks leave it undefined. For related tools, see the Root Calculator and the Log Calculator, which undo exponents.