Find (2 × 107) + (3 × 104).
a) 2.003 × 104
b) 2.003 × 107
c) 2.03 × 104
d) 2.03 × 107

Step-by-step explanation:

I'm assuming that you need to be able to do this off of a calculator so that's the way I'm going to show you.

We have 10 to the 7th in one term and 10 to the 4th in the other term.  We need to break up the 10 to the 7th into a power that matches the smaller one.  10^7 = 10^4*10^3 since, when we have like bases (which we do; it's 10), we add the exponents together.  Rewriting our original in terms of that like power:

(2 × 10⁴ × 10³) + (3 × 10⁴)

We can now factor out the 10⁴ since it is common in both sets of parenthesis to get:

10⁴(2 × 10³ + 3)

What's inside that set of parenthesis needs to be expanded now.  2 × 10³ is 2000, and add 3 to that and you get 2003.  NOW what we have is

2003 × 10⁴

But that's not in correct scientific notation form, so we need to move the decimal over 3 places to left, adding 3 to the exponent of 4 we already have.  That gives us, in the end, finally:

2.003 × 10⁷

Choice B.