Question

How do you multiply `(3 x 10^7)(5 x 10^4)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`3 xx 10^7 xx 5 xx 10^4 =>`

`3 xx 5 xx 10^7 xx 10^4 =>`

`15 xx 10^7 xx 10^4`

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))`

`15 xx 10^color(red)(7) xx 10^color(blue)(4) =>`

`15 xx 10^(color(red)(7) + color(blue)(4)) =>`

`15 xx 10^11`

If it is necessary to write the solution in correct scientific notation we need to move the decimal point 1 place to the left so we need to add 1 to the 10s exponent:

`15 xx 10^11 =>`

`1.5 xx 10^12`