Enter a base and an exponent to calculate base raised to the power of the exponent. The Exponent Calculator returns the result along with a step-by-step breakdown — supports positive, negative, decimal, and zero exponents. Also try the calculate Logarithm Result (y), log₁₀(x) & ln(x) — Natural Log — Logarithm (log).
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An exponent (also called a power) indicates how many times a base number is multiplied by itself. For example, 2³ means 2 × 2 × 2 = 8. The notation aⁿ represents the base 'a' raised to the power 'n'.
Any non-zero number raised to the power of 0 equals 1. For example, 5⁰ = 1 and 100⁰ = 1. The expression 0⁰ is mathematically indeterminate, though it is often treated as 1 in combinatorics and some other fields.
A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent. For example, 2⁻³ = 1 / 2³ = 1 / 8 = 0.125. Negative exponents represent fractions rather than negative results.
Yes. Decimal exponents are fully supported — enter the decimal form of any fraction as the exponent. For example, an exponent of 0.5 is equivalent to a square root, so 9^0.5 = 3. An exponent of 0.333... is equivalent to a cube root.
When multiplying two powers that share the same base, you add the exponents: aⁿ × aᵐ = a^(n+m). For example, 2² × 2⁴ = 2^(2+4) = 2⁶ = 64.
When dividing two powers that share the same base, you subtract the exponents: aⁿ ÷ aᵐ = a^(n−m). For example, 3⁵ ÷ 3² = 3^(5−2) = 3³ = 27.
Yes, negative bases are supported. Keep in mind that a negative base raised to an even exponent yields a positive result, while a negative base raised to an odd exponent yields a negative result. For example, (−2)³ = −8, but (−2)⁴ = 16.
Multiplication is repeated addition (3 × 4 = 3 + 3 + 3 + 3), while exponentiation is repeated multiplication (3⁴ = 3 × 3 × 3 × 3 = 81). Exponentiation grows much faster than multiplication as numbers increase.