Question

How do you simplify `\frac { 8.2\times 10^ { - 5} } { - 2\times 10^ { - 9} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`8.2/-2 xx 10^-5/10^-9 =>`

`-4.1 xx 10^-5/10^-9`

We can now use this rule for exponents to simplify the 10s terms:

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

`-4.1 xx 10^color(red)(-5)/10^color(blue)(-9) =>`

`-4.1 xx 10^(color(red)(-5)-color(blue)(-9)) =>`

`-4.1 xx 10^(color(red)(-5)+color(blue)(9)) =>`

`-4.1 xx 10^4`

If we want to write this in standard form we need to move the decimal point 4 places to the right because the exponent of the 10s term is positive:

`-4.1 xx 10^4 = -41000`