29. \( \begin{array}{l}\text { MP) Critique Reasoning Tim was asked } \\ \text { to find the difference of } 5.9 \times 10^{7} \text { and } \\ 2.4 \times 10^{7} \text {. His work is shown here. Did he } \\ \text { find the difference correctly? If so, name } \\ \text { the mathematical properties he used. If } \\ \text { not, explain his error and find the correct } \\ \text { difference. } \\ \end{array}=\left(5.9 \times 10^{\top}\right)-\left(2.4 \times 10^{\top}\right) \)

Tim was asked to compute (5.9 × 10⁷) – (2.4 × 10⁷). Notice that both terms have the common factor 10⁷. Tim’s work shows that he subtracted the coefficients (5.9 – 2.4) and then kept the common factor, which is the correct procedure. Specifically, using the distributive property, we have:   (5.9 × 10⁷) – (2.4 × 10⁷) = (5.9 – 2.4) × 10⁷ = 3.5 × 10⁷. Thus, Tim’s work is correct. The mathematical properties he used are:  • The distributive property: factoring out the common multiplier (10⁷) from both terms.  • Subtraction of like terms: subtracting the coefficients when the exponential part is the same. The correct difference is 3.5 × 10⁷.