Question 1: Calculate: (3 × 10^4) × (2 × 10^3).

Answer: 6 × 10^7

Question 2: Divide: (8 × 10^6) ÷ (4 × 10^2).

Answer: 2 × 10^4

Question 3: Express in standard form: 0.00056 × 3,000.

Answer: 1.68 × 10^{-1}

Question 4: Calculate: (5 × 10^3) ÷ (2 × 10^2).

Answer: 25

Question 1: Calculate: (7 × 10^2) × (3 × 10^3).

Answer: 2.1 × 10^6

Question 2: Divide: (9 × 10^5) ÷ (3 × 10^2).

Answer: 3 × 10^3

Question 1: A car accelerates from 2 × 10^2 km/h to 1 × 10^3 km/h. Express the increase in speed in standard form and calculate the difference.

Answer: 8 × 10^2 km/h

Question 2: A scientist needs 3 × 10^4 grams of a chemical. If a container holds 6 × 10^3 grams, how many containers are needed? Express your answer as a standard form number.

Answer: 5 × 10^0

Question 1: An astronomer observes a star with a luminosity of 4 × 10^25 watts. A second instrument detects a luminosity of 1 × 10^24 watts. How many times brighter is the first star compared to the second?

Answer: 40

Question 2: A factory produces 2 × 10^6 items per year. If production doubles, express the new annual production in standard form.

Answer: 4 × 10^6

Question 1: Calculate: (5 × 10^3) × (2 × 10^4) ÷ (1 × 10^2).

Answer: 1 × 10^6

Question 2: A bacteria population starts at 3 × 10^2 and doubles every hour. Express the population after 4 hours in standard form.

Answer: 4.8 × 10^3

Question 1: Express in standard form: 0.0007 × 4,500.

Answer: 3.15 × 10^{-1}

Question 2: Divide: (6 × 10^4) ÷ (3 × 10^2).

Answer: 200

Question 1: A student calculates: (4 × 10^3) × (2 × 10^2) = 8 × 10^5. What is wrong, and what is the correct answer?

Answer: Incorrect; should be 8 × 10^5, but actually the correct answer is 8 × 10^5 (so the original is correct).

Question 2: A student divides: (9 × 10^4) ÷ (3 × 10^3) = 3 × 10^0, but their work shows 3 × 10^1. Identify and fix the mistake.

Answer: They forgot to subtract exponents; correct answer is 3 × 10^1.