Question

How many mobile phones can a manufacturing company produce in 2000 days if it can produce
$4\times {10}^5$ phones every day?

• A. $8\times {10}^8$
• B. $8\times {10}^{12}$
• C. $8\times {10}^5$
• D. $8\times {10}^{15}$

Answer 1

The correct option is A $8\times {10}^8$

Number of mobile phones produced in 1 day $=4\times {10}^5$
2000 can be written as $2\times {10}^3$
Number of mobile phones produced in 2000 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 product rule of exponents, $a^m\times a^n=a^{m+n}$
$=8\times ({10}^3\times {10}^5)=8\times {10}^{3+5}$
$=8\times {10}^8$
Therefore, $8\times {10}^8$ mobile phones can be produced by the manufactures in 2000 days.