Question

How to simplify `(6.2 times 10^3)(2 times 10^4)` in scientific notation?

Answer 1

It is `1.24xx10^8`

Explanation:

First thing is to multiply the mantisses (`6.2xx2`) and the exponents. There you use the property of exponents: `a^b*a^c=a^(b+c)`.

So first you get: `(6.2xx10^3)(2xx10^4)=12.4xx10^7`

In scientiffic notation the rule is that mantisse has to be between 0 and 10, so you have to move the decimal point one place left increasing the exponent by 1 at the same time. Finally you get the answer: `1.24xx10^8`