Question

What is `(7.35*10^5)(8.40*10^4)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(7.35 * 8.40)(10^5 * 10^4) =>`

`61.74(10^5 * 10^4)`

Next, 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))`

`61.74(10^color(red)(5) * 10^color(blue)(4)) =>`

`61.74 * 10^(color(red)(5)+color(blue)(4)) =>`

`61.74 * 10^9`

Now, to write this in scientific notation we must move the decimal point 1 place to the left so we need to add `1` to the 10s exponent:

`61.74 * 10^9 => 6.174 * 10^10`