Calculate powers, find bases or exponents, with support for negative and fractional exponents.
Quick Answer:Enter a base and exponent to calculate the power instantly. Results shown in both standard and scientific notation, with square root and cube root equivalents.
Calculation Result
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Standard Notation
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Scientific Notation
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Square Root of Result
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Cube Root of Result
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Exponential growth is often underestimated. The "rule of 72" lets you quickly estimate doubling time: divide 72 by the growth rate percentage. At 6% annual growth, something doubles in about 12 years. Understanding exponents is critical for compound interest, population growth, viral spread modeling, and computational complexity analysis in algorithms.
Any non-zero number raised to the power of zero equals 1. This is because x^n / x^n = x^(n-n) = x^0, and any number divided by itself is 1. The special case 0^0 is typically defined as 1 by convention in combinatorics and computer science, though it is sometimes considered indeterminate in mathematical analysis.
A negative exponent means you take the reciprocal of the base raised to the positive exponent. So x^(-n) = 1 / x^n. For example, 2^(-3) = 1/2^3 = 1/8 = 0.125. This is consistent with the rule x^a / x^b = x^(a-b) and useful for expressing very small numbers.
Raising a negative number to a fractional exponent can produce complex (imaginary) numbers. For example, (-1)^0.5 = i (the square root of -1). However, some fractional exponents with odd denominators do have real results: (-8)^(1/3) = -2 (cube root). Most calculators return NaN or an error for negative bases with non-integer exponents in the real number domain.