Answer
(a) $ 2.56 *10^{-9}mm^3 $
(b) $2.56 * 10^{-10} L $ (the book incorrectly omits the 2.56)
Work Step by Step
$(a)$
To convert cubic μm to cubic mm we multiply by the conversion factor for micro- to milli- and then cube.
Since $\mu$(micro-) $= 10^{-6}$ and $m$(milli-) = $10^{-3}$ so there are $10^3 \mu m$ in 1$mm$
$2.56 \mu m^3 * \dfrac{(1mm)}{( 10^3 \mu m)^3}$
Distribute the exponent remembering that when we raise an exponent by another exponent we multiply them together.
$2.56 \mu m^3 * \dfrac{1mm^3}{( 10^{(3*3)} \mu m^3)}$
$2.56 \mu m^3 * \dfrac{1mm^3}{( 10^{9} \mu m^3)}$
Recall that $\dfrac{1}{x^2}$ = $x^{-2}$ and cancel the units
$$2.56 *10^{-9}mm^3$$
$(b)$
For this step want to know the volume of $10^5$ cells in $L$ (liters). Recall that $1L = 1dm^3$.
Since deci- = $10^{-1}$ and milli- = $10^{-3}$ there are $10^2mm$ in $1 dm$.
$2.56 *10^{-9}mm^3 * 10^5 * \dfrac{(1dm)^3}{(10^{2}mm)^3}$
$2.56 *10^{-9}mm^3 * 10^5 * \dfrac{1dm^3}{10^{(2*3)}mm^3}$
$2.56 *10^{-9}mm^3 * 10^5 * \dfrac{1dm^3}{10^{(6)}mm^3}$
$2.56 *10^{-9} * 10^5 * 10^{-6} dm^3$
$2.56 * 10^{(-9+5-6)} dm^3 $
$$2.56 * 10^{-10} L$$
