Question 1: Express 48 as a product of primes using index notation.

Answer: 2^4 × 3

Question 2: Write the prime factorization of 125 in index notation.

Answer: 5^3

Question 3: Calculate 2^5 × 2^3 using index notation and simplify the result.

Answer: 2^8

Question 4: A business increases its investment by a factor of 3^4 each year. How much does the investment grow after 3 years?

Answer: 81

Question 5: Express 16,384 as a power of 2 using index notation.

Answer: 2^14

Question 6: A company's revenue doubles every year. If the initial revenue is represented as 2^5, what is the revenue after 4 years?

Answer: 2^9

Question 7: Construct a power expression to represent the prime factorization of 360.

Answer: 2^3 × 3^2 × 5

Question 8: A financial analyst models a population growth with the expression 5^x. If the population reaches 625, what is the value of x?

Answer: 4

Question 9: Identify the mistake: Simplify 2^3 × 2^2 as 2^5, but students write 2^6. Which step is incorrect?

Answer: Incorrect application of the rule for multiplying powers; it should be 2^(3+2) = 2^5.

Question 10: Express 48 as a product of primes and then write it in index notation.

Answer: 2^4 × 3, so 48 = 2^4 × 3

Question 11: A company's profit growth is modeled as 2^x, where x increases annually. After 5 years, the profit is 32. Find x and express it in index notation.

Answer: x=5, so profit is 2^5