Exponent Calculator
Enter a base and an exponent and the calculator returns b raised to the power n. Works for positive, negative, integer and fractional exponents, with automatic scientific-notation output for extreme results.
2 ^ 10
1,024
- Base (b)
- 2
- Exponent (n)
- 10
- Result (b^n)
- 1,024
Raises the base b to the power of the exponent n. Positive integer exponents are repeated multiplication; negative exponents are reciprocals; fractional exponents are roots (e.g. b^0.5 = √b). Very large or very small results switch to scientific notation.
How to use this calculator
Type the base into the first field and the exponent into the second. The result updates as you type. Negative exponents return reciprocals (2^-3 = 0.125). Fractional exponents return roots (4^0.5 = 2, 8^(1/3) = 2). Results larger than 10^15 or smaller than 10^-4 switch to scientific notation so the display stays readable.
How the calculation works
The calculator evaluates b^n using IEEE-754 double-precision arithmetic — the same standard as scientific calculators and spreadsheets. Two edge cases are excluded: a negative base with a non-integer exponent has no real-number value (the answer is complex), and zero raised to a negative exponent implies division by zero. In both cases the calculator returns an explanatory message rather than a number. The 0^0 case follows the standard convention used by combinatorics and IEEE-754, returning 1.
Worked example
For 2^10: the result is 1,024. For 2^-3: 1 ÷ 2^3 = 1 ÷ 8 = 0.125. For 4^0.5: √4 = 2. For 10^9: 1,000,000,000 (one billion). For 2^50: 1.125900 × 10^15, large enough that the calculator switches to scientific notation.
Frequently asked questions
What does a negative exponent mean?
A negative exponent flips the base to a reciprocal: b^-n = 1 ÷ b^n. So 2^-3 = 1 ÷ 8 = 0.125, and 10^-6 = 1 ÷ 1,000,000 = 0.000001. Negative exponents are how scientific notation expresses very small numbers (1 nanometre = 10^-9 metres).
What does a fractional exponent mean?
A fractional exponent is a root. b^(1/2) is the square root of b; b^(1/3) is the cube root; b^(p/q) is the q-th root raised to the power p. For example, 9^0.5 = √9 = 3, and 27^(1/3) = ³√27 = 3. Decimal exponents follow the same rule — 2^1.5 = 2 × √2 ≈ 2.828.
Why does the calculator reject a negative base with a fractional exponent?
Because the result is not a real number. (-4)^0.5 asks for the square root of -4, which is the imaginary number 2i. (-8)^(1/3) is more subtle: there is a real cube root, -2, but other fractional powers of negative numbers give complex results, so the calculator refuses the whole class rather than pretending to handle only some cases. For integer exponents — (-2)^3 = -8, (-2)^4 = 16 — negative bases work fine.
What is 0^0?
Strictly, 0^0 is an indeterminate form: the limit depends on the path. In practice almost every standard returns 1, including IEEE-754 floating-point arithmetic (used by every modern programming language and spreadsheet) and the binomial theorem in combinatorics, where 0^0 = 1 makes the formula consistent. This calculator follows that convention and returns 1.
Why does the result switch to scientific notation?
Numbers with magnitude ≥ 10^15 or < 10^-4 are hard to read in full — 2^50 written out is 1,125,899,906,842,624, and 10^-9 is 0.000000001. Scientific notation (mantissa × 10^exponent) shows the same value with the magnitude up front, which is how scientific calculators, physics textbooks and engineering output do it.
How accurate is the result?
Calculations use IEEE-754 double-precision floats, accurate to about 15–17 significant digits. For very large integer powers (e.g. 2^53 and above), the result loses precision and only the leading digits are exact — this is why the calculator switches to scientific notation. For everyday algebra and scientific work that range is far beyond what you need.