Exponent Calculator
An exponent is repeated multiplication in shorthand: two raised to ten is ten factors of two, one superscript digit replacing all that writing. Powers appear in growth, areas, volumes, decibels and bits — the arithmetic is rarely the hard part, knowing what happens at the extremes is. This page returns the value beside its scientific notation, staying honest when a power has no real answer or no representable one.
Enter values
Results
- Value
- 1,024
- In scientific notation
- 1.024e+3
How is the Exponent calculated?
Enter the base — any number, decimals and negatives allowed — and the exponent, anywhere from −100 to 100. Whole exponents multiply repeatedly, while fractional exponents take roots, so 9 raised to 0.5 is the square root of 9. The lead row prints the value to four decimal places, and the second shows it in scientific notation where very large and very small powers stay readable. Undefined inputs — zero to a negative power, or a negative base to a fractional power — are stated in words instead.
Formula
b^e means b multiplied by itself e times when e is whole; a fractional exponent takes a root instead, so b^(1/n) is the n-th root of b. b is the base, e the exponent. Zero to a negative power divides by zero, and a negative base to a fractional power has no real root — both are refused. The rest runs in double precision: 2^10 is exactly 1,024.
Example
Raise 2 to the power of 10 and the page reads 1,024.0000 with 1.024e+3 beside it — the shorthand computers use once digits run long. Growth behaves identically: 1.08 raised to 10 comes out at 2.1589, so an 8% annual rate roughly doubles an amount in nine years. On the small side, 2 to the −10 reads 0.001 to four decimals — better from the notation row as 9.766e-4. Enter 1e160 as the base with exponent 2: the true value exceeds double precision, so the page says so rather than printing infinity.
Things to remember
Exponents are where modest inputs stop being modest: each doubling is one more turn of the power, and logarithms read such scales backwards. Watch the extremes, not the middles — naming an undefined power or an overflow in plain words beats a wall of digits pretending to precision they lack.
Frequently Asked Questions
What does a negative exponent mean?
Reciprocal multiplication: two raised to −10 is one divided by two raised to 10, or 0.0009765625. The base stays put and only the direction flips, which is why sub-unit powers of two appear constantly in computing, information theory and finance.
What is zero to the power of zero?
This calculator follows the standard convention and reports 1, because x to the 0 equals 1 for every other base and consistency wins. Zero to a negative power is a different matter — that divides by zero — so the page refuses that case in words.
How do you type scientific notation into the form?
Use the e form coders do: 1e150 for 1 followed by 150 zeros, or 2.5e-3 for 0.0025. Every number field here accepts it, which is far quicker and safer than counting zeros by hand into a figure that may already have lost one.
Why does my result say too large to display?
The power exceeded the largest number a browser can hold, roughly 1.8 × 10^308, and would have collapsed to infinity. The page admits the limit instead — a smaller base, a smaller exponent, or reading the result as scientific notation brings it back into range.
Related Calculators
- Modulo CalculatorMath & ArithmeticFind the remainder and whole quotient of a division, with the full equation written out so a = quotient × b + remainder can be checked.
- Prime Number CalculatorMath & ArithmeticCheck whether a number is prime, see its smallest prime factor and find the next prime that follows it.
- Number Base ConverterUnit ConvertersTurn a decimal number into binary, octal and hexadecimal, with worked examples for 255, colour codes and IPs.
- Rule of 72 CalculatorFinance & InterestEstimate how long an investment takes to double, with the exact doubling time shown beside the rule of 72.