nth power (xⁿ)
Raise a number to any integer power, including negative exponents.
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Co je nth power
The nth power means multiplying a number n times: xⁿ = x · x · … · x (n factors). The number x is the base, n is the exponent. The calculator also handles negative exponents.
Where it is used in practice
- Compound interest – money grows as a power (after n years the initial amount is multiplied by (1+rate)ⁿ).
- Computing: capacity grows as a power of two (n bits = 2ⁿ values).
- Exponential growth of populations, spread of diseases or viral content.
Good to know
A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. The zeroth power is always 1: x⁰ = 1 (for x ≠ 0).
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.