For questions 37-42, evaluate each expression. Write all answers in scientific notation. 37. \( \left(5.8 \times 10^{7}\right)\left(6 \times 10^{2}\right) \) 38. \( \left(3.7 \times 10^{-6}\right)\left(2.9 \times 10^{6}\right) \) \( \square \) 39. \( \left(2 \times 10^{3}\right) \div\left(6.4 \times 10^{9}\right) \) 40. \( \frac{1.9 \times 10^{5}}{2.5 \times 10^{-9}} \) 41. \( \left(4.5 \times 10^{-6}\right)+\left(9.2 \times 10^{-7}\right) \) 42. \( \left(3.1 \times 10^{6}\right)-\left(4.7 \times 10^{4}\right) \)

Below are the step‐by‐step calculations and answers in scientific notation: 37. (5.8×10⁷)(6×10²)  • Multiply the coefficients: 5.8×6 = 34.8  • Multiply the powers of 10: 10⁷×10² = 10^(7+2) = 10⁹  • Thus: 34.8×10⁹. To convert to proper scientific notation, shift the decimal: 34.8 = 3.48×10¹, so the answer becomes 3.48×10¹⁰. 38. (3.7×10⁻⁶)(2.9×10⁶)  • Multiply the coefficients: 3.7×2.9 = 10.73  • Multiply the powers of 10: 10^(–6)×10⁶ = 10^(–6+6) = 10⁰ = 1  • Thus: 10.73×1 = 10.73. In scientific notation, write 10.73 as 1.073×10¹. 39. (2×10³) ÷ (6.4×10⁹)  • Divide the coefficients: 2÷6.4 = 0.3125  • Subtract exponents for the powers of 10: 10^(3–9) = 10^(–6)  • Thus: 0.3125×10⁻⁶. Adjust to proper scientific notation by writing 0.3125 = 3.125×10⁻¹, so the answer is 3.125×10^(–1–6) = 3.125×10⁻⁷. 40. (1.9×10⁵) ÷ (2.5×10⁻⁹)  • Divide the coefficients: 1.9÷2.5 = 0.76  • Subtract exponents: 10^(5–(–9)) = 10^(5+9) = 10¹⁴  • Thus: 0.76×10¹⁴. Adjust to scientific notation: 0.76 = 7.6×10⁻¹ so the result is 7.6×10^(14–1) = 7.6×10¹³. 41. (4.5×10⁻⁶) + (9.2×10⁻⁷)  • To add, write both terms with the same power of 10. Convert 9.2×10⁻⁷ to 0.92×10⁻⁶.  • Now add the coefficients: 4.5 + 0.92 = 5.42  • Therefore, the answer is 5.42×10⁻⁶. 42. (3.1×10⁶) – (4.7×10⁴)  • Convert 4.7×10⁴ to exponent 10⁶: 4.7×10⁴ = 0.047×10⁶.  • Subtract the coefficients: 3.1 – 0.047 = 3.053  • Thus, the answer is 3.053×10⁶. Final Answers: 37. 3.48×10¹⁰ 38. 1.073×10¹ 39. 3.125×10⁻⁷ 40. 7.6×10¹³ 41. 5.42×10⁻⁶ 42. 3.053×10⁶