Add `6.75 xx (10^3) cm` to `4.52 xx (10^2) cm` with regard to significant figures.

Explanation

To solve the problem of adding \(6.75 \times 10^3 \, \text{cm}\) and \(4.52 \times 10^2 \, \text{cm}\) while considering significant figures, follow these steps:

### Step 1: Convert to the same power of ten
To add the two numbers, they must be expressed in the same power of ten. The second number, \(4.52 \times 10^2 \, \text{cm}\), can be converted to the same power of ten as the first number.

\[ 4.52 \times 10^2 \, \text{cm} = 0.452 \times 10^3 \, \text{cm} \]

### Step 2: Add the two numbers
Now that both numbers are expressed in terms of \(10^3\), we can add them together:

\[ 6.75 \times 10^3 \, \text{cm} + 0.452 \times 10^3 \, \text{cm} = (6.75 + 0.452) \times 10^3 \, \text{cm} \]

Calculating the sum:

\[ 6.75 + 0.452 = 7.202 \]

Thus, we have:

\[ 7.202 \times 10^3 \, \text{cm} \]

### Step 3: Consider significant figures
Now, we need to round the result according to significant figures. The number \(6.75\) has three significant figures, and \(0.452\) has three significant figures as well. When adding, the result should be rounded to the least number of decimal places from the original numbers.

In this case, \(6.75\) has two decimal places, and \(0.452\) has three decimal places. Therefore, we round our result \(7.202\) to two decimal places:

\[ 7.20 \times 10^3 \, \text{cm} \]

### Final Answer
The final answer is:

\[ \boxed{7.20 \times 10^3 \, \text{cm}} \]