General power (xʸ)
Raise a number to any real exponent, including negative and fractional.
Graf funkce
Co je general power
A general power xʸ allows any real exponent – integer, negative or fractional. A fractional exponent corresponds to a root: x^(1/2) = √x, x^(1/3) = ∛x.
Where it is used in practice
- Scientific and engineering calculations where the exponent is not an integer.
- Finance – converting an interest rate to another period (e.g. annual to monthly via the power 1/12).
- Physics – power laws (air resistance, scaling).
Good to know
A negative base with a fractional exponent generally has no real result (e.g. (−4)^0.5 = √−4 is not a real number).
Rules of exponents
When working with powers it helps to know the basic rules, which always hold:
xⁿ · xᵖ = xⁿ⁺ᵖ (product – add the exponents)
xⁿ ÷ xᵖ = xⁿ⁻ᵖ (quotient – subtract the exponents)
(xⁿ)ᵖ = xⁿ·ᵖ (power of a power – multiply)
x⁻ⁿ = 1 / xⁿ (negative exponent)
x^(1/n) = ⁿ√x (root as a power)
In detail with examples: rules of exponents.
Tip: very large numbers are shown in shortened form – use scientific notation.