Question

How do you calculate `(4 times 10 ^-3 )/(8 times 10^-7)`?

Answer 1

`5.0xx10^3`

Explanation:

`(color(blue)(4xx10^(-3)))/(color(red)(8xx10^(-7)))" "=" "color(blue)((4xxcolor(red)(10^7))/(color(red)(8)xx10^3) )`

`=4/8xx10^4`

`=0.5xx10^4`

As the question's format is of a particular style we should write our answer in the same format (scientific notation).

But written in scientific notation we need 5.0 and not 0.5

so we write `0.5` as `" "5.0xx1/10`

Putting it all together we have:

`5.0xx1/10xx10^4`

`5.0xx10^3`

Answer 2

See the entire solution process below:

Explanation:

First, rewrite this expression as:

`(4/8)(10^-3/10^-7) = 0.5 xx (10^-3/10^-7)`

Now, use this rule of exponents to simplify the 10s terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`0.5 xx (10^color(red)(-3)/10^color(blue)(-7)) = 0.5 xx x^(color(red)(-3)-color(blue)(-7)) = 0.5 xx 10^(color(red)(-3)+color(blue)(7)) =`

`0.5 xx 10^4`

Or

`5.0 xx 10^3`

Or

`5,000`