Star Shining Bright

Classical Mechanics Level pending

A cepheid variable star's brightness can be predicted by observing the period over which its luminosity varies.

A particular cepheid variable is found by this method to have a luminosity of \(4\times 10 ^ {31} \text{ W}\). The intensity of its light on Earth is \(0.00025 \text{ W/m}^2\). How far away is the star in metres?