Cube (x³)
Calculate the cube of a number. With graph, explanation and real-world examples.
Graf funkce
Co je cube
Cubing a number means multiplying it three times: x³ = x · x · x. It is read “x cubed”. The result is called a cube because it gives the volume of a cube with edge x.
Where it is used in practice
- Volume of a cube or sphere – volume grows with the cube of the dimension (twice as big = eight times the volume).
- Scaling volume and mass when resizing models and sculptures.
- Physics and chemistry – density, concentration and radiation laws.
Good to know
Unlike squaring, cubing keeps the sign: (−2)³ = −8. That is why the cube root of a negative number has one real solution.
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.