Exponent Calculator
Enter a base and an exponent and press Calculate. The exponent can be a whole number, a decimal or a negative number, so 5 to the power −2 and 2 to the power 0.5 both work. A negative base takes whole-number exponents only. With a decimal exponent it has no real-number result, and the calculator says so instead of showing a number. The result prints in full, with commas and up to 6 decimal places, and in scientific notation and e-notation with up to 6 significant figures. A result too small for 6 decimals or too large for full digits prints in scientific notation alone.
Calculate baseexponent
How to use the Exponent Calculator
- Enter your numbers in the Exponent Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The exponent rules
x^a × x^b = x^(a+b) · · · (x^a)^b = x^(ab) · · · x^(-a) = 1/x^a · · · x^(1/n) = ⁿ√x
An exponent counts repeated multiplication. A negative exponent inverts the base, and a fractional exponent is a root. Any non-zero base to the power 0 equals 1.
Worked example
2^10 = 1,024. 5^−2 = 1/5² = 0.04. A root is a decimal exponent, so 9^0.5 = 3, the square root of 9. 2^10 also prints as 1.024 × 10^3 and 1.024e+3. 1.05^20 shows as 2.653298, the growth factor of 5% compounded for 20 periods. A cube root needs 1/3, which you can only type as a decimal, so 8^0.333333 shows 1.999999 rather than 2.
Frequently asked questions
What is 0⁰?
Some branches of mathematics leave it undefined, while combinatorics and the binomial theorem treat it as 1. This calculator returns 1.
How are very large or very small results displayed?
Up to about 1.8 × 10^308 in size, in full with commas and at most 6 decimal places, beside the scientific notation. 10^20 prints as 100,000,000,000,000,000,000 and 1 × 10^20. A result below 0.0000005, such as 10^−7, prints as 1 × 10^−7 alone, because 6 decimals would round it to 0. Past 1.8 × 10^308 the full digits no longer fit, so 2^1024 prints as 1.79769 × 10^308 alone. That figure comes from logarithms, and they hold six figures up to about 10^10,000,000 in size. Past that you get a message. So does 0 to a negative power, which would mean dividing by 0. To convert a number you already have, use the Scientific Notation Calculator.
Can I use it for x^(1/2)?
Yes. Type the exponent as a decimal: 0.5 for a square root, 0.25 for a fourth root. A negative base with a decimal exponent gets a message instead of a number, because the result is not a real number. That includes (−8)^0.333333. The cube root of −8 is −2, but 0.333333 is not exactly 1/3, so there is no real result. For an odd root of a negative number, enter the base without its minus sign and put the minus sign in front of the result.