Unable to process Large numbers

Question

A small spherical cell of diameter $1.616E^{-35}$ is exponentially multiplying as $2^n$ where n is the generation number. The duration of 1 generation is $5.39E^{-44}$ second. And the cells cluster closely to form a big sphere.
(a) How many cells exist after 13.79 billion years and what diameter sphere will they form?
(b) If radius is increasing at speed of light how fast is the surface area and volume of big sphere increasing?

Answer 1

(a) The age of the universe is about $4.3\cdot 10^{17}$ seconds, which is about $8\cdot 10^{60}$ Planck times (aka. generations). Raising $2$ to the power of this large number results in a number with $\approx 8\cdot 10^{60}\cdot\log_{10}2\approx 2.4\cdot 10^{60} $ digits. The radius (or diameter or any reasonable multiple of either) of a sphere is approximately the cube root of this number times the Planck langth, so a $\approx .8\cdot 10^{60}$ digit number times $\approx 10^{-35}$ meters - but that factor merely scratches off 35 digits from our number, hence the radius still has $\approx .8\cdot 10^{60}$ digits when expressed in meters (or any other comprehensible unit anywhere from Planck length via meter and furlong and parsec to diameter-of-the-visible-universe).

(b) This part deals with much smaller growth. Just plug $r=ct$ into the surface and volume formula to see that the surface grows quadratic ovre time and volume grows cubic over time.