Question

How do you write the answer in scientific notation given `(3.7times10^-5)^2`?

Answer 1

See a solution process below:

Explanation:

We can rewrite this expression as:

`(3.7 xx 10^-5)^2 => (3.7 xx 10^-5) xx (3.7 xx 10^-5) =>`

`(3.7 xx 3.7) xx (10^-5 xx 10^-5) => 13.69 xx (10^-5 xx 10^-5)`

We can now 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))`

`13.69 xx (10^color(red)(-5) xx 10^color(blue)(-5)) = 13.69 xx 10^(color(red)(-5) + color(blue)(-5)) =>`

`13.69 xx 10^-10`

To write this in true scientific notation we need to move the decimal point 1 place to the left so we can add `1` to the exponent for the 10s term:

`13.69 xx 10^-10 => 1.369 xx 10^-9`