4) \( \left(17 \times 10^{3}\right)-\left(5 \times 10^{2}\right)-10^{4} \)

To simplify the expression \( \left(17 \times 10^{3}\right)-\left(5 \times 10^{2}\right)-10^{4} \), we first convert each term to the same power of ten, preferably \( 10^{4} \): 1. Convert \( 17 \times 10^{3} \) to the same power: \[ 17 \times 10^{3} = 1.7 \times 10^{4} \] 2. Convert \( 5 \times 10^{2} \): \[ 5 \times 10^{2} = 0.05 \times 10^{4} \] 3. Keep \( 10^{4} \) as is. Now we can rewrite the original expression: \[ (1.7 \times 10^{4}) - (0.05 \times 10^{4}) - (1 \times 10^{4}) \] Combine the coefficients: \[ (1.7 - 0.05 - 1) \times 10^{4} \] Calculating the coefficients: \[ 1.7 - 0.05 = 1.65 \] \[ 1.65 - 1 = 0.65 \] So we have: \[ 0.65 \times 10^{4} = 6.5 \times 10^{3} \] Thus, the simplified expression is: \[ 6.5 \times 10^{3} \]