Question

How do you simplify `(8\times 10^ { 5} ) \div ( 4\times 10^ { - 3} )`?

Answer 1

`2xx10^8`

Explanation:

Using the `color(blue)"law of exponents"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^m/a^n=a^(m-n))color(white)(2/2)|)))`

`(8xx10^5)÷(4xx10^-3)" can be expressed as a fraction"`

`"That is " (8xx10^5)/(4xx10^-3)`

The fraction can be `color(blue)"split up"` as follows.

`rArr8/4xx10^5/10^-3`

`=2xx10^((5-(-3)))larr" using above law "`

`=2xx10^8`

Answer 2

`2 xx 10^8`

Explanation:

`(8 xx 10^5)-:(4 xx 10^-3)`

`:.(8 xx 100000)-:(4 xx 0.001)`

`:.=(800000)-:(0.004)`

`:.800000/0.004`

`:.=200,000,000`

`:.=2 xx 10^8`