Exponent Calculator
Raise any base to any power, including negative and fractional exponents.
About Exponent Calculator
An exponent tells you how many times to multiply a number (the base) by itself. Positive integer exponents are straightforward repeated multiplication. A negative exponent means 'take the reciprocal': b^(−n) = 1/bⁿ. A fractional exponent is a root: b^(1/2) is the square root, b^(1/3) the cube root, b^(p/q) is the q-th root of bᵖ. Negative bases with even-denominator fractional exponents produce complex (imaginary) numbers.
Formulas
Integer exponent
b^n = b × b × … × b (n times)
- b
- Base
- n
- Integer exponent
Negative exponent
b^(−n) = 1 / b^n
Fractional exponent
b^(p/q) = q-th root of b^p
Worked example
With the default values below, Exponent Calculator returns Result of 1,024.0000000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Base (b)
- 2
- Exponent (n)
- 10
Results
- Result
- 1,024.0000000000
Step by step
- 1Repeated multiplication (10 times)= 1024
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is b⁰?
Any non-zero base raised to the power of zero equals 1. The special case 0⁰ is mathematically indeterminate, but by convention most calculators and programming languages return 1.
What does a negative exponent mean?
A negative exponent means 'divide one by the positive power': 2^(−3) = 1 / 2³ = 1/8 = 0.125. It does not make the result negative.
Can I raise a negative number to a fractional power?
Only when the denominator of the fraction is odd. (−8)^(1/3) = −2 because (−2)³ = −8. (−4)^(1/2) would require the square root of a negative number, which is an imaginary number (2i), not a real number.