Calculate a base raised to any exponent, including negative exponents (reciprocals) and fractional exponents (roots).
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A positive integer exponent means repeated multiplication: base^n means the base multiplied by itself n times, for example 2^5 = 2×2×2×2×2 = 32. A negative exponent means the reciprocal of the positive version: base^(−n) = 1 ÷ base^n. A fractional exponent represents a root: base^(1/2) is the square root of the base, base^(1/3) is the cube root, and so on.
Raising a negative number to a fractional exponent doesn't always produce a real number result, for example, (−4)^0.5 would be the square root of a negative number, which isn't a real number. This calculator will let you know when a combination you've entered has no real number result.
2^10 = 2×2×2×2×2×2×2×2×2×2 = 1024, ten repeated multiplications by the base. 2^(−3) is the reciprocal of 2^3: 1 ÷ (2×2×2) = 1 ÷ 8 = 0.125. And 16^0.5 (a fractional exponent of 1/2) means the square root of 16, which is 4.
Treating a negative exponent as making the result negative, it doesn't, base^(−n) is a reciprocal (1 ÷ base^n), which stays positive for a positive base, for example 2^(−3) = 0.125, not −8.
Expecting a real number result from a negative base raised to a non-integer exponent, like (−4)^0.5, that's the square root of a negative number, which has no real number result, this calculator will flag it rather than silently returning something misleading.
Mixing up base and exponent order when reading a formula, base^exponent means the base multiplied by itself exponent times, not the other way around, 2^10 (1024) is very different from 10^2 (100).
Any non-zero number raised to the power of 0 equals 1, by mathematical convention, this comes from consistently extending the pattern of dividing successive powers of the same base.
A negative exponent flips the base into a fraction: base^(−n) equals 1 divided by base^n. For example, 2^(−3) = 1 ÷ 2^3 = 1/8 = 0.125.
A decimal exponent represents a root, base^0.5 is the same as the square root of the base, base^(1/3) (approximately 0.333) is the cube root, and so on, following the general rule base^(1/n) equals the nth root of the base.
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