Exponent Calculator
Calculate powers and exponents
Fast, accurate calculations with clear results. Built for speed and ease of use.
Formula
base^exponentHow to Use Exponent Calculator
- Enter the required values in the input fields.
- Review the formula and methodology used.
- Check the calculated results below.
- Use the results for your specific needs.
Examples
An exponent tells you how many times to multiply a base by itself, and the rules extend cleanly past positive whole numbers into zero, negative, and fractional exponents, each of which means something specific rather than being a special case to memorise separately.
The formula
b^n = b x b x ... x b (n times), extended by b^0 = 1, b^-n = 1/b^n, b^(1/n) = nth root of b- b
- the base
- n
- the exponent
Worked example
2^3 = 2 x 2 x 2 = 8, the plain repeated-multiplication case. 2^0 = 1, by the rule that any nonzero base to the power 0 equals 1, which keeps the pattern 2^3, 2^2, 2^1, 2^0 consistent as each step divides the previous result by 2: 8, 4, 2, 1. 2^-3 = 1 / 2^3 = 1/8 = 0.125, continuing the same halving pattern below zero, and 2^(1/2) = sqrt(2) is approximately 1.4142136, since a fractional exponent of 1/n means the nth root.
What trips people up
- b^0 = 1 holds for every nonzero base, including large or small numbers; 0^0 is the one case left undefined, treated differently across different fields of maths.
- A negative exponent does not make the result negative, it makes it a reciprocal; 2^-3 is a small positive fraction, 0.125, not -8.
- (-2)^2 and -2^2 are different: parentheses around the negative base give a positive 4, while no parentheses applies the exponent before the negative sign, giving -4.
- Fractional exponents combine a root and a power; 8^(2/3) means the cube root of 8, which is 2, then squared, giving 4, and doing the operations in the other order gives the same answer but can be harder to compute by hand.
Frequently asked questions
- Why is anything to the power of 0 equal to 1?
- It keeps the pattern of dividing by the base consistent as the exponent decreases by one each step; b^3, b^2, b^1, b^0 each divides the previous result by b, and 1 is what falls out at the bottom of that pattern.
- What does a fractional exponent like 1/2 actually mean?
- It means a root. b^(1/2) is the square root of b, b^(1/3) is the cube root, and in general b^(1/n) is the nth root of b.
- Why is a negative exponent a fraction rather than a negative number?
- The negative sign in the exponent means 'take the reciprocal', not 'make the result negative'; 2^-3 is 1/8, a small positive number, not -8.
- How do I calculate an exponent like 8^(2/3) by hand?
- Split it into a root and a power in either order: take the cube root of 8 first, which is 2, then square it, giving 4, or square 8 first and take the cube root of the result, which also gives 4.
- What happens with a negative base and a fractional exponent?
- It often has no real answer; (-8)^(1/2) asks for a real square root of a negative number, which does not exist, even though (-8)^(1/3), a cube root, does exist and equals -2.