Exponent Calculator
Calculate any base raised to any power, including negative, zero, and fractional exponents.
Rules for working with exponents
A few key rules make exponents easier to work with: any nonzero number raised to the power of 0 equals 1, a negative exponent means taking the reciprocal (x^-n = 1/x^n), and a fractional exponent represents a root — x^(1/2) is the same as the square root of x.
When multiplying two powers with the same base, you add the exponents (x^a × x^b = x^(a+b)); when dividing, you subtract them. These rules extend naturally to more complex algebraic expressions.
Where exponents show up in real life
Exponents underpin compound interest and investment growth calculations, exponential population or bacterial growth models, the inverse-square law in physics, and computer science concepts like binary representation and algorithmic complexity (Big O notation).
Very large or very small exponents can produce results too large or small to display precisely — for extreme values, scientific notation becomes necessary to represent the result meaningfully.
Frequently asked questions
What does a negative exponent mean?
A negative exponent means taking the reciprocal of the positive-exponent result — for example, 2^-3 equals 1/(2^3), or 1/8.
What does a fractional exponent mean?
A fractional exponent represents a root — x^(1/2) is the square root of x, x^(1/3) is the cube root, and so on.