📚 Part 1: Multiple Choice

Directions: Circle the correct answer for each question.

1. Which expression is equivalent to 3⁻²?

−9

1/9

−6

9

2. Which of the following is the correct way to rewrite x⁻⁵ with a positive exponent?

−x⁵

x⁵

1/x⁵

5/x

3. What is the value of 2⁻⁴?

−8

1/16

−16

1/8

4. Which expression is equivalent to 1/a³?

a³

−a³

a⁻³

3a

✏️ Part 2: Simplify and Convert

Directions: Rewrite each expression using only positive exponents, then simplify where possible. Show your work in the space provided.

5. Rewrite with a positive exponent: m⁻⁷ = _____________

6. Simplify: 5⁻³ = _____________

7. Simplify and rewrite with positive exponents: 4x⁻²y³ = _____________

8. Simplify: (2a⁻¹)(3a⁻²) = _____________

9. Evaluate: 10⁻³ = _____________

🧠 Part 3: Application Problems

Directions: Read each problem carefully and show all your work.

10. A scientist measures a bacterium that is 5⁻³ centimetres wide. Write this measurement as a fraction and as a decimal. Which is easier to work with, and why?

11. Simplify the following expression completely, writing your answer with positive exponents only:

(x³ · x⁻⁵) / x⁻¹ = _____________

12. A student says that 4⁻² = −16 because "a negative exponent makes the answer negative." Explain the error in the student's thinking and provide the correct answer.