Question 1: Calculate the value of 2^{-3}.

Answer: 0.125

Question 2: Simplify the expression: 5^{-2} × 5^{3}.

Answer: 5^{1}

Question 3: Evaluate 10^{-4} and express your answer as a decimal.

Answer: 0.0001

Question 4: Calculate the value of (3^{-2})^{3}.

Answer: 3^{-6}

Question 5: Express 1/8 as a power of 2 with a negative index.

Answer: 2^{-3}

Question 6: If x = 2^{-2} and y = 2^{3}, find the value of x × y.

Answer: 2^{1}

Question 7: Solve for n: 4^{n} = 4^{-3}.

Answer: -3

Question 8: Construct a triangle on the grid where the side lengths are proportional to the powers 2^{3} and 2^{-2}.

Answer: Students draw a triangle with sides proportional to 8 and 1/4, demonstrating understanding of negative indices in scale factors.

Question 9: Evaluate the expression: (2^{4} ÷ 2^{6})^{-2}.

Answer: 2^{4}

Question 10: Identify and correct the mistake in evaluating 3^{-2} + 3^{2} as 9 + 1.

Answer: Incorrect; 3^{-2} = 1/9, not 9. The correct sum is 1/9 + 9.

Question 11: Using laws of indices, simplify: (2^{-3})^{2} × 2^{4}.

Answer: 2^{-2}

Question 12: A scientist uses the expression 10^{-x} to model decreasing quantities. If the quantity halves when x increases by 1, find the value of x.

Answer: 1