Question 1: Express 48 as a product of prime factors in index notation.

Answer: 2^4 × 3

Question 2: Write 125 in exponential form using prime factors.

Answer: 5^3

Question 3: Simplify the expression: 2^5 × 2^3.

Answer: 2^8

Question 4: Calculate the value of 3^4 × 3^2.

Answer: 243

Question 1: Express the number 360 in prime factorization using index notation. Then, write the total exponent sum of all prime factors.

Answer: {"exponentSum":6,"primeFactorization":"2^3 × 3^2 × 5"}

Question 2: If 2^x × 3^y = 48, find x and y. Show your working and express the answer in index notation.

Answer: {"x":4,"y":1,"indexForm":"2^4 × 3"}

Question 1: A factory produces 2^5 × 3^2 pieces per day. How many pieces are produced in 7 days? Express your answer in index notation.

Answer: 2^5 × 3^2 × 7

Question 2: A researcher has a DNA sample with 2^3 × 5^2 base pairs. If a mutation doubles the number of base pairs of prime factor 2, what is the new total? Express in index notation.

Answer: 2^4 × 5^2

Question 1: Express 1024 as a power of 2. Then, verify if 1024 can be written as 2^x and find x.

Answer: {"x":10,"power":"2^10"}

Question 2: Construct a number with prime factors 2, 3, and 5 such that the total exponent sum is 8. Provide the prime factorization in index notation.

Answer: 2^3 × 3^2 × 5^3

Question 1: Simplify: 2^6 ÷ 2^3.

Answer: 2^3

Question 2: Express 1/8 as a power of 2 in index notation.

Answer: 2^−3

Question 3: Identify the error in the statement: 3^2 × 3^3 = 3^5.

Answer: Incorrect, because 3^2 × 3^3 = 3^{2+3} = 3^5, which is correct. If an error existed, students must identify it.