Systematic selection for applications requiring multiple criteria is more complex. For example, when the material should be both stiff and light, for a rod a combination of high Young's modulus and low density indicates the best material, whereas for a plate the "cube root" of stiffness divided by density formula_1 is the best indicator, since a plate's bending stiffness scales by its thickness cubed. Similarly, again considering both stiffness and lightness, for a rod that will be pulled in tension the specific modulus, or modulus divided by density formula_2 should be considered, whereas for a beam that will be subject to bending, the material index formula_3 is the best indicator.