Question

How do you simplify and write `(2 times 10^4)(4.1 times 10^3)` in scientific notation?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(2 xx 4.1)(10^4 xx 10^3) => 8.2(10^4 xx 10^3)`

Now, use this rule for exponents to complete the simplification:

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

`8.2(10^color(red)(4) xx 10^color(blue)(3)) => 8.2 xx 10^(color(red)(4) +color(blue)(3)) => 8.2 xx 10^7`