If
$\left( { 100 }^{ 20 } \right) ^{ 5 }$
is
**
expanded
**
. How many
**
digits
**
will you have?

102
200
100
201

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The number of digits $n$ of a number $N$ is given by:

$\begin{aligned} n & = \log_{10} N + 1 \\ & = \log_{10} \left(100^{20}\right)^5 + 1 \\ & = \log_{10} \left(10^{40}\right)^5 + 1 \\ & = \log_{10} 10^{200} + 1 \\ & = 200 + 1 \\ & = \boxed{201} \end{aligned}$ .