How many mobile phones can a manufacturer produce in $2,000$ days if it can produce $4\times {10}^5$ phones everyday?

The correct option is B $8\times {10}^8$
Given:
Number of mobile phones produced in $1$ day $=4\times {10}^5$

To Find:
Number of mobile phones produced in $2,000=2\times {10}^3$ days.

$\therefore$ Number of mobile phones produced in $2\times {10}^3$ days $=2\times {10}^3$ $\times$ Number of mobile phones produced in $1$ day
$=2\times {10}^3\times 4\times {10}^5$
$=2\times 4\times {10}^3\times {10}^5$
$=(2\times 4)\times ({10}^3\times {10}^5)$
$=8\times ({10}^3\times {10}^5)$

Applying the multiplication rule for same base and different exponents: $a^m\times a^n=a^{m+n}$

$=8\times {10}^{(3+5)}$
$=8\times {10}^8$

Therefore, $8\times {10}^8$ mobile phones can be produced by the manufacturer in $2,000$ days.

Hence, option (b.) is the correct one.