Let's solve the given expression:

$(3.5 \times 10^7) + (2.4 \times 10^8)$

Since the terms have different powers of 10, we must adjust them so they have the same power of 10.

$3.5 \times 10^7 = 0.35 \times 10^8$

Now, the expression becomes:

$(0.35 \times 10^8) + (2.4 \times 10^8)$

We can factor out $10^8$:

$(0.35 + 2.4) \times 10^8 = 2.75 \times 10^8$

So, the final answer in standard index form is:

$2.75 \times 10^8$

Let me know if you'd like more details or if you have any questions!

Here are some related questions:

1. What is the general process for adding numbers in scientific notation?
2. How do you convert between different powers of 10?
3. Can you subtract numbers in scientific notation using a similar method?
4. Why do we factor out powers of 10 when adding or subtracting in standard form?
5. How do you multiply or divide numbers in scientific notation?

Tip: When adding or subtracting numbers in scientific notation, always ensure that the powers of 10 are the same before performing the operation!