1. **Problem statement:** Calculate the values of $$A = 85.7 \times 10^{4} + 45 \times 10^{11}$$ and $$B = \frac{0.6 \times (10^{3})^{2} \times 6 \times 10^{4}}{9 \times 10^{5}}$$ and express the results in scientific notation. 2. **Calculate A:** First, write both terms with powers of 10 clearly: $$85.7 \times 10^{4} = 8.57 \times 10^{5}$$ (since $85.7 = 8.57 \times 10^{1}$, so $85.7 \times 10^{4} = 8.57 \times 10^{1+4} = 8.57 \times 10^{5}$) The second term is already: $$45 \times 10^{11} = 4.5 \times 10^{12}$$ (since $45 = 4.5 \times 10^{1}$) Now add: $$A = 8.57 \times 10^{5} + 4.5 \times 10^{12}$$ Since $10^{12}$ is much larger than $10^{5}$, the sum is dominated by the larger term: $$A \approx 4.5 \times 10^{12}$$ 3. **Calculate B:** Calculate numerator: $$(10^{3})^{2} = 10^{6}$$ So numerator: $$0.6 \times 10^{6} \times 6 \times 10^{4} = 0.6 \times 6 \times 10^{6+4} = 3.6 \times 10^{10}$$ Denominator: $$9 \times 10^{5}$$ Divide numerator by denominator: $$B = \frac{3.6 \times 10^{10}}{9 \times 10^{5}}$$ Cancel common factors: $$B = \frac{\cancel{3.6} \times 10^{10}}{\cancel{9} \times 10^{5}} \times \frac{1}{\frac{9}{3.6}} = \frac{0.4 \times 10^{10}}{10^{5}}$$ More precisely: $$\frac{3.6}{9} = 0.4$$ So: $$B = 0.4 \times 10^{10-5} = 0.4 \times 10^{5}$$ Rewrite in scientific notation: $$0.4 = 4.0 \times 10^{-1}$$ So: $$B = 4.0 \times 10^{-1} \times 10^{5} = 4.0 \times 10^{4}$$ 4. **Final answers:** $$A \approx 4.5 \times 10^{12}$$ $$B = 4.0 \times 10^{4}$$ These are the results in scientific notation.