Mathematics

Problem

A solid cube

C_{1}

has volume

128\,\text{cm}^{3}

. Another cube

C_{2}

has volume

2^{-3}\times128\,\text{cm}^{3}

. a. (i) Find the volume of

C_{2}

. b. (ii) Determine the edge length of each cube, leaving your answers in exponential form with base

2

. c. (iii) Express the ratio

\dfrac{\text{edge of }C_{2}}{\text{edge of }C_{1}}

in the form

2^{k}

and state the value of

k