The problem is asking to add two numbers in scientific notation and write the answer also in scientific notation.

The expression provided is:

$(4.6 \times 10^3) + (8 \times 10^3)$

Step-by-step solution:

1. Recognize that both terms have the same exponent: $10^3$, so we can factor out $10^3$.

   $(4.6 \times 10^3) + (8 \times 10^3) = (4.6 + 8) \times 10^3$

2. Add the coefficients:

   $4.6 + 8 = 12.6$

3. Rewrite the result:

   $12.6 \times 10^3$

4. Convert the answer into proper scientific notation: To express $12.6 \times 10^3$ in proper scientific notation, the coefficient must be between 1 and 10. So, rewrite $12.6$ as $1.26 \times 10^1$.

   $12.6 \times 10^3 = 1.26 \times 10^1 \times 10^3 = 1.26 \times 10^4$

Final Answer:

$1.26 \times 10^4$

Would you like further clarification on any step or details?

Here are 5 related questions for practice:

1. How do you multiply numbers in scientific notation?
2. What is the process for subtracting numbers in scientific notation with different exponents?
3. How do you convert a large number into scientific notation?
4. What are the rules for adding numbers with different powers of 10?
5. How do you handle division in scientific notation?

Tip: When adding or subtracting in scientific notation, always ensure the powers of 10 are the same before combining the coefficients.