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To solve \((8.1 \times 10^5) + (4 \times 10^5)\), let's follow these steps:

1. **Identify common terms:** Both terms have the same power of \(10^5\). Therefore, we can combine them by adding the coefficients.

2. **Add the coefficients:** 
   \[
   8.1 + 4 = 12.1
   \]

3. **Multiply by \(10^5\):**
   \[
   12.1 \times 10^5
   \]

So, the answer in standard index form is:
\[
\mathbf{1.21 \times 10^6}
\]

Would you like more details on any step or have any questions?

Here are some additional related questions:
1. How would you add numbers in scientific notation with different powers of 10?
2. What is the standard form of \( (3.6 \times 10^4) + (5.4 \times 10^4) \)?
3. How do you multiply two numbers in scientific notation?
4. What is the process to convert a large number like 1,210,000 into scientific notation?
5. How would you solve \( (2.5 \times 10^3) - (1.2 \times 10^3) \)?

**Tip:** When adding or subtracting in scientific notation, ensure the exponents match before combining the coefficients.

Learn how to add numbers in scientific notation, such as (8.1 × 10^5) + (4 × 10^5), by following a step-by-step solution. Suitable for students in Grades 8-10.

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