To do this without a calculator, I would change: 5.2 × 10^(-2) to ... 52×10^(-3)
--> then multiply the whole numbers 52 × 8 = 416
--> next add the exponents on the tens. -3 + -4 = -7
= 416×10^(-7)
* now they'll want you to move the decimal back to behind the first digit. (just standard convention)
= 4.16×10^(-5)
If you have a calculator you can just use the "EE" button for ×10^power typed in it looks like this :
5.2 EE -2 × 8 EE -4 =
then make sure your calculator is in scientific mode, otherwise you'll be counting decimal spaces
