Chapter 5 Polynomials and Polynomial Functions - 5.1 Use Properties of Exponents - 5.1 Exercises - Problem Solving - Page 335: 54a

$\frac{1}{125}$

Using the equation for the volume of a sphere: $\frac{V_{inner core}}{V{Earth}}=\frac{\frac{4}{3}(\frac{1}{5}r)^3\pi}{\frac{4}{3}r^3\pi}=\frac{(\frac{1}{5}r)^3}{r^3}=\frac{\frac{1}{125}r^3}{r^3}=\frac{1}{125}$