Exponent Calculator
With base 2, exponent 10, exponent comes to 1,024 — result. It is reached in 6 steps, the last of which is pow(2, 10), and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Digital Library of Mathematical Functions §4.2, not an approximation fitted to it.
A number raised to any power, including negative and fractional ones, with the root it is equivalent to and the answer in scientific notation.
Formula and sources checked · How we check
Base 2, Exponent 10
1,024
Result for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Result
pow(2, 10)1,024- The negative power, base^(−n)
1 / 10240.001- Equivalent root
1 / 100.1- Order of magnitude
floor(log10(1024))3- Mantissa in scientific notation
1024 / pow(10, 3)1.024- Digits before the decimal point
floor(log10(1024)) + 14
Worked example
2 to the tenth is 1,024 — the reason a kilobyte was 1,024 bytes rather than 1,000, and the reason a thousandfold and a 2^10-fold are close enough to be confused for each other in computing.
How to work it out yourself
- 1.Enter the base and the exponent. A negative exponent gives the reciprocal — 2 to the −3 is one eighth, not minus eight.
- 2.A fractional exponent is a root: 0.5 is a square root, 1/3 a cube root. The root line above says which.
- 3.Read the scientific notation line for very large or very small results, where the digit count matters more than the digits.
The formula
- Result
pow(2, 10) - The negative power, base^(−n)
1 / 1024 - Equivalent root
1 / 10 - Order of magnitude
floor(log10(1024)) - Mantissa in scientific notation
1024 / pow(10, 3) - Digits before the decimal point
floor(log10(1024)) + 1
Source: NIST Digital Library of Mathematical Functions §4.2 — powers, roots and logarithms
Questions people actually ask
- What does a negative exponent mean?
- One over the positive power. 2 to the −3 is 1 ÷ 2³ = 0.125. It follows from the rule that dividing subtracts exponents: 2³ ÷ 2⁵ is 2⁻², and it also equals 8 ÷ 32 = 0.25, which is 1 ÷ 2². The sign says which side of the fraction bar the power sits on, not that the answer is negative.
- Why is anything to the power of zero equal to one?
- Because dividing a power by itself subtracts the exponents to zero and divides the number by itself to one. 5³ ÷ 5³ is both 5⁰ and 125 ÷ 125. The convention is not arbitrary — it is the only value that keeps the exponent rules consistent.
- What is a fractional exponent?
- A root. x^(1/2) is the square root, x^(1/3) the cube root, and x^(2/3) is the cube root squared. It follows from multiplying exponents: (x^(1/2))² = x¹, so x^(1/2) must be the number that squares to x. That is also why a negative base with a fractional exponent usually has no real value.
- How large can a result get?
- Past about 10^308 the answer leaves the range double-precision floating point can represent and becomes infinity. Below about 10^−308 it collapses to zero. Those limits are the machine’s rather than mathematics’, which is why the digit count is printed above — a number too large to store is still a number you can describe.
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