Sure! Here is a sample unit test on exponent rules. It includes a variety of question types such as multiple-choice, true/false, and open-ended questions to assess understanding of exponent rules.
Exponent Rules Unit Test
Name: ___________________
Date: ___________________
Section 1: Multiple Choice (1 point each)
-
What is \( a^m \cdot a^n \)?
- A) \( a^{m+n} \)
- B) \( a^{m-n} \)
- C) \( a^{mn} \)
- D) \( a^{m/n} \)
-
What is \( (a^m)^n \)?
- A) \( a^{m+n} \)
- B) \( a^{mn} \)
- C) \( a^{m/n} \)
- D) \( a^{m-n} \)
-
What happens when you multiply powers with the same base?
- A) You add the exponents.
- B) You subtract the exponents.
- C) You multiply the bases.
- D) None of the above.
-
What is the value of \( 2^{-3} \)?
- A) 8
- B) \( \frac{1}{8} \)
- C) -8
- D) -\( \frac{1}{8} \)
Section 2: True/False (1 point each)
-
\( a^{-m} = \frac{1}{a^m} \)
True / False -
\( a^0 = 0 \)
True / False -
\( a^{m/n} = \sqrt[n]{a^m} \)
True / False
Section 3: Short Answer (2 points each)
-
Simplify \( x^3 \cdot x^{-5} \).
Answer: ________________________________
-
Simplify \( (3x^2)^3 \).
Answer: ________________________________
-
Evaluate \( \frac{y^4}{y^2} \).
Answer: ________________________________
Section 4: Application (3 points each)
-
If \( a^2 = 16 \), what is the value of \( a^5 \)? Show your work.
Answer: ________________________________
-
Simplify the expression \( \frac{(4x^3y^{-2})^2}{16x^4y} \).
Answer: ________________________________
Answer Key (for the instructor)
Section 1:
- A
- B
- A
- B
Section 2:
5. True
6. False
7. True
Section 3:
8. \( x^{-2} \) or \( \frac{1}{x^2} \)
9. \( 27x^6 \)
10. \( y^2 \)
Section 4:
11. \( a^2 = 16 \) implies \( a = 4 \), thus \( a^5 = 4^5 = 1024 \).
12. \( \frac{(4^2(x^3)^2(y^{-2})^2)}{16x^4y} = \frac{16x^6y^{-4}}{16x^4y} = x^{6-4}y^{-4-1} = x^2y^{-5} \) or \( \frac{x^2}{y^5} \).
Feel free to modify the questions or format as needed!