Exponent Calculator
Exponent Calculator
Enter a base and an exponent to calculate the result. This handles positive, negative, fractional, and zero exponents, and flags the rare case where a negative base with a non-whole exponent has no real-number result.
Positive integer exponents are just repeated multiplication (2^10 means multiplying 2 by itself ten times), while negative exponents flip the result into a reciprocal — 2^(−2) equals 1 divided by 2², or 0.25. Any nonzero number raised to the power of 0 always equals exactly 1, a rule that can look surprising at first but falls directly out of the pattern of dividing consecutive powers of the same base by one another. Fractional exponents connect this whole system to roots — a base raised to the power 1/2 is the same as its square root.
- Positive integer exponents: base^n means multiplying the base by itself n times — 2^10 = 2×2×2×2×2×2×2×2×2×2 = 1024.
- Negative exponents mean reciprocals: base^(−n) = 1 ÷ base^n, so 2^(−2) = 1 ÷ 4 = 0.25.
- Any nonzero number to the power of 0 equals 1: this is a mathematical convention (0^0 is typically also treated as 1 by this calculator, following common convention, though it is debated in some contexts).
What does a fractional exponent mean?
A fractional exponent represents a root — base^(1/2) is the square root of the base, base^(1/3) is the cube root, and more generally base^(m/n) is the nth root of base raised to the m power.
Why does a negative base with a fractional exponent sometimes show "undefined"?
When the base is negative and the exponent isn't a whole number, the result is a complex number rather than a real one (e.g. (−2)^0.5 has no real square root) — this calculator flags that case rather than returning a misleading value.
Exponent Calculator
Enter a base and an exponent to calculate the result. This handles positive, negative, fractional, and zero exponents, and flags the rare case where a negative base with a non-whole exponent has no real-number result.
Positive integer exponents are just repeated multiplication (2^10 means multiplying 2 by itself ten times), while negative exponents flip the result into a reciprocal — 2^(−2) equals 1 divided by 2², or 0.25. Any nonzero number raised to the power of 0 always equals exactly 1, a rule that can look surprising at first but falls directly out of the pattern of dividing consecutive powers of the same base by one another. Fractional exponents connect this whole system to roots — a base raised to the power 1/2 is the same as its square root.
- Positive integer exponents: base^n means multiplying the base by itself n times — 2^10 = 2×2×2×2×2×2×2×2×2×2 = 1024.
- Negative exponents mean reciprocals: base^(−n) = 1 ÷ base^n, so 2^(−2) = 1 ÷ 4 = 0.25.
- Any nonzero number to the power of 0 equals 1: this is a mathematical convention (0^0 is typically also treated as 1 by this calculator, following common convention, though it is debated in some contexts).
What does a fractional exponent mean?
A fractional exponent represents a root — base^(1/2) is the square root of the base, base^(1/3) is the cube root, and more generally base^(m/n) is the nth root of base raised to the m power.
Why does a negative base with a fractional exponent sometimes show "undefined"?
When the base is negative and the exponent isn't a whole number, the result is a complex number rather than a real one (e.g. (−2)^0.5 has no real square root) — this calculator flags that case rather than returning a misleading value.