How this calculator works
A positive whole exponent is repeated multiplication: 2¹⁰ = 2 × 2 × … × 2 = 1,024.
A negative exponent is the reciprocal: 2⁻³ = 1 ÷ 2³ = 0.125.
A fractional exponent is a root: 9^0.5 = √9 = 3, and 8^(1/3) = 2.
Any non-zero number to the power 0 is 1. Very large or small results are shown in scientific form.
Worked example
2 to the power 10
- 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
- Result: 1,024.
- Scientific form: 1.024 × 10³.
Questions people ask
What are the main exponent rules?
Multiply same bases by adding exponents (aᵐ × aⁿ = aᵐ⁺ⁿ), divide by subtracting, and raise a power to a power by multiplying (aᵐ)ⁿ = aᵐⁿ.
Why is a negative base with a fractional exponent a problem?
It asks for an even root of a negative number, which has no real answer. For example, (−4)^0.5 is not a real number.
What is 0 to the power 0?
It is usually defined as 1 in algebra and combinatorics, though in some contexts it is left undefined.
How do exponents relate to logarithms?
They are inverses: if 2¹⁰ = 1,024, then log₂(1,024) = 10. The log calculator does the reverse.
Last reviewed October 2, 2026