Question 1: Calculate 2^4.

Answer: 16

Question 2: Calculate 3^3.

Answer: 27

Question 3: Evaluate 2^5 × 2^3.

Answer: 256

Question 4: Simplify 3^2 × 3^4.

Answer: 243

Question 1: If 2^x = 32, what is the value of x? Explain how you find it.

Answer: x=5

Question 2: A computer uses 2^n bits of data. If it uses 1024 bits, find the value of n. Show your working.

Answer: n=10

Question 3: A rectangular grid has side lengths of 2^3 and 2^4 units. What is the total number of small squares in the grid? Explain your reasoning.

Answer: 128

Question 4: Express 81 as a power of 3. Show your work.

Answer: 3^4

Question 1: A bacteria population doubles every hour. If starting with 1 bacteria, how many bacteria will there be after 6 hours? Express your answer using powers.

Answer: 2^6

Question 2: A security system encrypts data using 2^n bits. If the system uses 256 bits, what is n? Show your working.

Answer: n=8

Question 1: Prove that 2^a × 2^b = 2^{a+b} for any integers a and b. Write a brief explanation.

Answer: Using properties of exponents.

Question 2: Find the value of the expression 2^{4} × 3^{2} + 2^{3} × 3^{3}. Explain your steps.

Answer: 16×4 + 8×27 = 64 + 216 = 280

Question 1: Calculate 2^3 × 2^4. A student says the answer is 2^7. Is this correct? Explain your reasoning.

Answer: Yes, because when multiplying powers with the same base, add exponents.

Question 2: Simplify 3^5 ÷ 3^2. A student writes the answer as 3^10. Is this correct? Why or why not?

Answer: No, because dividing powers with the same base, subtract exponents: 3^{5-2} = 3^3.