The formula
How it works
An exponent tells you how many times to multiply a number by itself. Enter a base and an exponent to get the result — the calculator handles whole, negative and fractional powers, and switches to scientific notation when the answer gets very large or very small.
FAQ
What does a negative exponent mean?
A negative exponent is a reciprocal: b⁻ⁿ equals 1 divided by bⁿ. So 2⁻³ is 1 ÷ 8 = 0.125. The power still applies, then the result is flipped.
What is anything to the power of zero?
Any non-zero number raised to the power 0 equals 1. It follows from the rule that dividing equal powers, like b² ÷ b², gives b⁰, and that must be 1.
What does a fractional exponent mean?
A fractional exponent is a root: b^(1/2) is the square root of b, and b^(1/3) is the cube root. More generally, b^(m/n) means take the nth root of b, then raise it to the mth power.
Can the base be negative?
Yes — a negative base raised to a whole-number exponent gives a positive result for even exponents and a negative result for odd ones, since the sign flips each time you multiply. Fractional exponents on a negative base can produce a result with no real value, which the calculator shows as a non-finite answer.
How do I multiply or divide two powers with the same base?
When the base is the same, multiplying powers adds the exponents (bᵐ × bⁿ = bᵐ⁺ⁿ) and dividing subtracts them (bᵐ ÷ bⁿ = bᵐ⁻ⁿ). This shortcut avoids expanding each power separately.
Why does the result switch to scientific notation?
Very large or very small results are shown as a number times a power of ten so they stay readable, instead of printing dozens of digits. The calculator switches automatically once the value is extremely large or extremely close to zero.
What is the difference between squaring and cubing a number?
Squaring raises a number to the power 2 (multiplying it by itself once, useful for area), while cubing raises it to the power 3 (multiplying it by itself twice, useful for volume). Both are just special cases of the same exponent rule.
About the exponent calculator
This calculator raises a base number to a power, also called exponentiation. Exponents are a shorthand for repeated multiplication: instead of writing 2 × 2 × 2 × 2, you write 2 raised to the 4th power. They appear all over maths and science, from area and volume to compound interest and the scale of the universe, so being able to compute them quickly is genuinely useful.
How to use it
Enter the base — the number you are multiplying — and the exponent, which is how many times. The calculator shows the result straight away. For example, 2 to the power 10 is 1,024, and 5 to the power 3 is 125. You can also use fractions and negatives: an exponent of 0.5 gives the square root, and a negative exponent gives a reciprocal. When the answer is enormous or tiny, it is shown in scientific notation so it stays readable.
The formula
Exponentiation is written , where is the base and is the exponent. For a whole-number exponent it means multiplying the base by itself times: . The rules extend naturally — , , and a fractional exponent is a root, so . Powers with the same base also combine: .
Where it is used
Exponents power (literally) a huge range of calculations. Compound interest grows money by a base raised to the number of years, and populations, radioactive decay and virus spread all follow exponential curves. Computing uses powers of two for memory sizes, and scientific notation uses powers of ten to write very large or very small numbers. Geometry uses squares for area and cubes for volume, and physics is full of inverse-square laws written as negative exponents.