The energy given off by a spherical star, such as our sun, is equal to \(\sigma A T^4\), where \(\sigma\) is a constant, \(A\) is the surface area of the star, and \(T\) is its temperature. Spherical star JZ114 has ten times the radius and half the temperature of our sun. What is the ratio of the energy JZ114 gives off to the energy our sun gives off? Express your answer as a common fraction.
