Question 1:
\[
\text{If } 2^x = 32, \text{ then what is the value of } x?
\]
\[
\text{(a) } 4, \quad \text{(b) } 5, \quad \text{(c) } 6, \quad \text{(d) } 3
\]
Answer: B
Question 2:
\[
\text{Simplify: } \frac{a^7}{a^4}.
\]
\[
\text{(a) } a^3, \quad \text{(b) } a^{11}, \quad \text{(c) } a^2, \quad \text{(d) } a^{-3}
\]
Answer: A
Question 3:
\[
\text{Which of the following is equal to } (3^4 \times 3^2)?
\]
\[
\text{(a) } 3^6, \quad \text{(b) } 3^8, \quad \text{(c) } 3^2, \quad \text{(d) } 3^{10}
\]
Answer: A
Question 4:
\[
\text{Solve: } (x^3)^4.
\]
\[
\text{(a) } x^7, \quad \text{(b) } x^{12}, \quad \text{(c) } x^{9}, \quad \text{(d) } x^{16}
\]
Answer: B
Question 5:
\[
\text{What is the value of } 5^0?
\]
\[
\text{(a) } 5, \quad \text{(b) } 0, \quad \text{(c) } 1, \quad \text{(d) } -1
\]
Answer: C
Question 6:
\[
\text{If } a^{-3} = \frac{1}{27}, \text{ then } a = ?
\]
\[
\text{(a) } 3, \quad \text{(b) } -3, \quad \text{(c) } \frac{1}{3}, \quad \text{(d) } 9
\]
Answer: A
Question 7:
\[
\text{Which of the following is equal to } \frac{x^5}{x^8}?
\]
\[
\text{(a) } x^3, \quad \text{(b) } x^{-3}, \quad \text{(c) } x^{13}, \quad \text{(d) } x^{40}
\]
Answer: B
Question 8:
\[
\text{Solve: } (2x^3 y^{-2})^2.
\]
\[
\text{(a) } 4x^6 y^{-4}, \quad \text{(b) } 2x^6 y^{-4}, \quad \text{(c) } 4x^6 y^4, \quad \text{(d) } 2x^3 y^{-4}
\]
Answer: A
Question 9:
\[
\text{Which of the following represents } (x^{-2} y^3)^2?
\]
\[
\text{(a) } x^{-4} y^6, \quad \text{(b) } x^4 y^{-6}, \quad \text{(c) } x^{-1} y^6, \quad \text{(d) } x^1 y^{-6}
\]
Answer: A
Question 10:
\[
\text{What is the simplified form of } (x^5 y^{-3})^{-2}?
\]
\[
\text{(a) } x^{-10} y^6, \quad \text{(b) } x^{10} y^{-6}, \quad \text{(c) } x^{-5} y^3, \quad \text{(d) } x^{5} y^{-3}
\]
Answer: A
Question 11:
\[
\text{If } (x^3 y^{-2})^4 = x^a y^b, \text{ then what are } a \text{ and } b?
\]
\[
\text{(a) } a=12, b=-8, \quad \text{(b) } a=3, b=2, \quad \text{(c) } a=4, b=8, \quad \text{(d) } a=-12, b=8
\]
Answer: A
Question 12:
\[
\text{What is the result of } (x^{-1} y^2 z^{-3})^3?
\]
\[
\text{(a) } x^{-3} y^6 z^{-9}, \quad \text{(b) } x^{3} y^{-6} z^{9}, \quad \text{(c) } x^{-3} y^6 z^{9}, \quad \text{(d) } x^3 y^{-6} z^{-9}
\]
Answer: A
Question 13:
\[
\text{Which of the following is the simplified form of } (2x^2 y^{-1})^{-3}?
\]
\[
\text{(a) } \frac{1}{8x^6 y^{-3}}, \quad \text{(b) } \frac{1}{8x^{-6} y^3}, \quad \text{(c) } \frac{1}{8x^6 y^3}, \quad \text{(d) } 8x^{-6} y^3
\]
Answer: C
Question 14:
\[
\text{If } 3^{2x} = 81, \text{ then what is the value of } x?
\]
\[
\text{(a) } 2, \quad \text{(b) } 3, \quad \text{(c) } 4, \quad \text{(d) } 5
\]
Answer: B
Question 15:
\[
\text{Which of the following is the correct result of } (x^2 y^{-3})^{-2}?
\]
\[
\text{(a) } x^{-4} y^6, \quad \text{(b) } x^4 y^{-6}, \quad \text{(c) } x^{-2} y^3, \quad \text{(d) } x^2 y^{-3}
\]
Answer: A
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