Reduce the expression using scientific notation and correct number of significant digits. $\left(4 \times 10^{2}\right)+$ $\left(2.6 \times 10^{3}\right)$
Use $10^{\wedge}$ format (i.e. $10^{\wedge} 2$ for 10 squared)
$3 \times 10^{\wedge} 3$
$3.000 \times 10^{\wedge} 3$
$3 \times 10^{\wedge}-3$

Step 1 ：The problem is asking to add two numbers that are in scientific notation. The first number is \(4 \times 10^{2}\) and the second number is \(2.6 \times 10^{3}\).

Step 2 ：To add these numbers, we need to make sure that the exponents of 10 are the same. In this case, the second number has a larger exponent, so we will need to adjust the first number to match it.

Step 3 ：We can do this by moving the decimal point in the first number one place to the left, which will increase the exponent by 1. This will give us \(0.4 \times 10^{3}\) for the first number.

Step 4 ：Then we can add the two numbers together. The result of adding the two numbers together is \(3000.0\), which can be written in scientific notation as \(3.0 \times 10^{3}\).

Step 5 ：However, the question also asks for the correct number of significant digits. The first number, \(4 \times 10^{2}\), has one significant digit, and the second number, \(2.6 \times 10^{3}\), has two significant digits.

Step 6 ：When adding or subtracting numbers, the result should have the same number of decimal places as the number with the least decimal places. In this case, both numbers have no decimal places, so the result should also have no decimal places.

Step 7 ：Therefore, the final answer should be \(3 \times 10^{3}\).

Step 8 ：Final Answer: \(\boxed{3 \times 10^{3}}\)