Question

How do you simplify `(3.8 * 10 ^-5) ( 2.8 * 10 ^-5)` in scientific notation?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`3.8 * 10^-5 * 2.8 * 10^-5 =>`

`3.8 * 2.8 * 10^-5 * 10^-5 =>`

`10.64 * 10^-5 * 10^-5`

Next, we can use this rule of exponents to multiply the 10s terms:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`10.64 * 10^color(red)(-5) * 10^color(blue)(-5) =>`

`10.64 * 10^(color(red)(-5)+(color(blue)(-5))) =>`

`10.64 * 10^(color(red)(-5)-color(blue)(5)) =>`

`10.64 * 10^-10`

To put this expression into scientific notation we need to move the decimal point 1 place to the left therefore we need to add `1` to the 10s exponent:

`10.64 * 10^-10 =>`

`1.064 * 10^(-10 + 1) =>`

`1.064 * 10^-9`