Question

How do you multiply `(4 x 10^3)(2 x 10^4)`?

Answer 1

`8*10^7`

Explanation:

Whenever we're multiplying numbers expressed in scientific notation, we can separate the expression into two parts:

• The whole number
• The power of `10`

We have the following:

`(color(blue)4*color(red)(10^3))(color(blue)2*color(red)(10^4))`

Which can be rewritten as

`(color(blue)(4*2))(color(red)(10^3*10^4))`

`4` times `2` is obviously `8`, and since we have the same base (`10`), we can just add the exponents. Thus, we have:

`8*10^7` as our final answer.

To clarify, all I did is separate the whole number from the exponential expression. We want to deal with the whole numbers separately from the exponents. That is the key realization here.

Hope this helps!