So, my textbook taught me in one of the steps add the exponents.
For example:
1.5 x 10^1 * 10^-7
1.5 x 10^-6

But, a problem of mine I have completed just got me confused because the answer I got isn't any of the answers available. It's a multiple choice. Here is my problem:

(2.5 x 10^-9) (1.5 x 10^3) = (2.5 * 1.5) (10^-9 * 10^3)
= 3.75 * 10^-6
= 3.75 x 10^1 * 10^-6
= 3.75 x 10^-5

Did I do something wrong? If so can someone explain this to me?

Question

So, my textbook taught me in one of the steps add the exponents.
For example: 
1.5 x 10^1 * 10^-7 
1.5 x 10^-6

But, a problem of mine I have completed just got me confused because the answer I got isn't any of the answers available. It's a multiple choice. Here is my problem:

(2.5 x 10^-9) (1.5 x 10^3) = (2.5 * 1.5) (10^-9 * 10^3)
= 3.75 * 10^-6
= 3.75 x 10^1 * 10^-6
= 3.75 x 10^-5

Did I do something wrong? If so can someone explain this to me?

anonymous · Answer

why did you add a 10^1 in the 3rd line of your equations.

anonymous · Answer

= 3.75 * 10^-6  
(this is without what @tomo said, u don't need the extra 10^1 which you added)

kirbykirby · Answer

Ya you can't introduce the extra 10^1... (unless you did it to both sides of the equality)

kirbykirby · Answer

However, it would be correct if you wrote = 3.75 x 10^1 * 10^-7

kirbykirby · Answer

Here you are breaking up the exponents. Like what your book example did (But this is not necessary to write because it is a longer expression)

anonymous · Answer

I addede the 10^1 because that's what my textbook said to do. So, I don't need to do that?

kirbykirby · Answer

The book didn't "add" the extra 10^1.. if you look carefully; the first is exponent ^-6, then they write ^1 and ^-7 (NOT ^-6)

kirbykirby · Answer

You have ^-6 and you introduce ^1 and wrote ^1 and ^-6

kirbykirby · Answer

The point of the example was to show you how to add the exponents together.

anonymous · Answer

Oh alright. I got it. Thank you so much!!

kirbykirby · Answer

np =)