To write the number 20,109 in expanded notation, we break it down based on its place values:
- The first digit (2) is in the thousands place, which represents 2,000.
- The second digit (0) is in the hundreds place, which represents 0.
- The third digit (1) is in the tens place, which represents 10.
- The fourth digit (0) is in the ones place, which represents 0.
- The last digit (9) is in the ones place, which represents 9.
So, the expanded notation of 20,109 would be:
\[ 2 \times 10^4 + 0 \times 10^3 + 1 \times 10^2 + 0 \times 10^1 + 9 \times 10^0 \]
Looking at your original expression:
\[ 2x? + 1x100 + 9x10 \]
The "2x?" corresponds to the thousands place for 20,109, which is \(2 \times 10^4\).
The correct answer from your options that would complete this expression is:
10 to the 4th power.
So, the completed expression would be:
\[ 2 \times 10^4 + 1 \times 100 + 9 \times 10 \]