Question

How do you multiply `(2.34 xx 10^-8) (5.7 xx 10^-4)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(2.34 xx 5.7)(10^-8 xx 10^-4) =>`

`13.338 xx (10^-8 xx 10^-4)`

Next, use this rule for exponents to multiply the 10s terms:

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

`13.338 xx (10^color(red)(-8) xx 10^color(blue)(-4)) =>`

`13.338 xx 10^(color(red)(-8)+color(blue)(-4)) =>`

`13.338 xx 10^-12`

Now, to put this in scientific notation we need to move the decimal point 1 place to the left so we need to add `color(red)(1)` to the exponent of the 10s term:

`1.3338 xx 10^(-12+color(red)(1)) =>`

`1.3338 xx 10^-11`