I see you've uploaded an image containing mathematical exercises that involve calculations and converting results into scientific notation. I'll analyze and solve each problem step-by-step.

Let’s proceed systematically by solving one problem at a time. Here's the solution to Exercise 2, Question 1 first:

Question 1:

$\frac{12^3 \times 25^2}{15^3 \times 83}$

Step 1: Simplify the numerator and denominator.

1. $12^3 = 12 \times 12 \times 12 = 1728$
2. $25^2 = 25 \times 25 = 625$
3. Multiply the results in the numerator: $1728 \times 625 = 1,080,000$
4. $15^3 = 15 \times 15 \times 15 = 3375$
5. The denominator becomes: $3375 \times 83 = 280,125$

Step 2: Divide numerator by denominator.

$\frac{1,080,000}{280,125} \approx 3.857$

Step 3: Express in scientific notation.

$3.857 \approx 3.86 \times 10^0$

Let me know if you'd like to see solutions for the remaining questions or if you need clarifications on any part!

Relative Questions:

1. What is scientific notation, and why is it useful for representing large or small numbers?
2. How do you simplify powers like $12^3$ or $25^2$ quickly?
3. How do you handle division with large numbers in scientific notation?
4. How can approximations impact the accuracy of scientific notation?
5. What steps are necessary to verify results in such problems?

Tip:

Always simplify each part (numerator and denominator) completely before dividing for accurate results in scientific notation.