Multiple Choice

1. Simplify the expression $3^2 \times 3^4$.

   $3^8$

   $3^{24}$

   $3^6$

   $9^6$

2. Simplify the expression $x^7 \cdot x^2$.

   $x^9$

   $x^5$

   $x^{14}$

   $2x^9$

3. Simplify the expression $\frac{5^7}{5^3}$.

   $5^{10}$

   $5^4$

   $1^4$

   $5^{21}$

4. Simplify the expression $\frac{y^{10}}{y^3}$ for $y \neq 0$.

   $y^{13}$

   $y^7$

   $y^{-7}$

   $y^{\frac{10}{3}}$

5. Simplify the expression $(2^3)^4$.

   $2^7$

   $8^4$

   $2^{64}$

   $2^{12}$

6. Simplify the expression $(a^5)^2$.

   $a^{25}$

   $2a^5$

   $a^7$

   $a^{10}$

7. Simplify the expression $(2x)^3$.

   $8x^3$

   $2x^3$

   $6x$

   $6x^3$

8. Simplify the expression $(3ab)^2$.

   $9a^2b^2$

   $6ab$

   $3a^2b^2$

   $9a^2b$

9. Simplify the expression $\left(\frac{m}{n}\right)^5$ for $n \neq 0$.

   $\frac{m}{n^5}$

   $mn^{-5}$

   $\frac{m^5}{n^5}$

   $\frac{m^5}{n}$

10. What is the value of $7^0$?

    $1$

    $7$

    $0$

    $\frac{1}{7}$

11. What is the value of $(x+y)^0$ for any non-zero values of $x$ and $y$?

    Undefined

    $x+y$

    $0$

    $1$

12. Express $4^{-2}$ as a fraction.

    $-16$

    $16$

    $\frac{1}{16}$

    $-\frac{1}{16}$

13. Rewrite $p^{-3}$ using a positive exponent.

    $\frac{1}{p^3}$

    $\frac{1}{-p^3}$

    $p^3$

    $-p^3$

14. Express $\left(\frac{2}{3}\right)^{-1}$ as a simplified fraction.

    $\frac{3}{2}$

    $-\frac{2}{3}$

    $\frac{2}{3}$

    $\frac{1}{6}$

15. Simplify the expression $\frac{4^5 \times 4^2}{4^3}$.

    $4^{20}$

    $4^4$

    $4^6$

    $4^{10}$

16. Simplify the expression $(x^3)^2 \cdot x^4$.

    $x^{10}$

    $x^{12}$

    $x^9$

    $x^{24}$

17. Simplify $m^5 \cdot m^{-2}$.

    $m^{-10}$

    $\frac{1}{m^3}$

    $m^3$

    $m^7$

18. Simplify $\frac{k^4}{k^{-1}}$ for $k \neq 0$.

    $k^{-3}$

    $k^3$

    $k^5$

    $\frac{1}{k^5}$

19. Simplify $y^0 \cdot y^6$.

    $y^0$

    $y^{60}$

    $1$

    $y^6$

20. Simplify the expression $\left(\frac{a^3b^{-2}}{ab^0}\right)^2$ for $a \neq 0, b \neq 0$.

    $\frac{a^4}{b^2}$

    $a^4b^4$

    $a^4b^{-4}$

    $\frac{a^4}{b^4}$

21. Simplify $\frac{(2^3)^2 \cdot 2^{-4}}{2^0}$.

    $2^{10}$

    $2^6$

    $2^2$

    $2^{-2}$

22. Simplify the expression $\frac{10x^5}{2x^{-2}}$ for $x \neq 0$.

    $5x^7$

    $5x^3$

    $8x^7$

    $5x^{-10}$

23. Simplify $\left(\frac{r^{-3}}{r^{-1}}\right)^2$ for $r \neq 0$.

    $\frac{1}{r^2}$

    $r^4$

    $\frac{1}{r^4}$

    $r^{-4}$

24. Simplify $(3x^2y^3)(2x^{-1}y^4)$.

    $6xy^7$

    $5xy^7$

    $6x^3y^{12}$

    $6x^1y^1$

25. Evaluate the expression $\frac{(5^2)^3 \cdot 5^{-1}}{5^4}$.

    $5^{-1}$

    $5^{11}$

    $5^2$

    $5^1$

26. Simplify the expression $\frac{(x^3 y^2)^2 \cdot x^5}{y^4 \cdot x^0}$ where $x \ne 0$ and $y \ne 0$.

    $x^{11}y^8$

    $x^{11}y^2$

    $x^{11}$

    $x^{10}y^2$

27. Evaluate the expression $(2^{-2} \cdot 4^2)^{-1} \cdot 8^3$.

    $128$

    $64$

    $32$

    $16$

28. Simplify the expression $\left(\frac{3a^2 b^{-3}}{9a^{-1} b^2}\right)^{-2}$. Assume $a \ne 0$ and $b \ne 0$.

    $\frac{9a^6}{b^{10}}$

    $\frac{9b^{10}}{a^6}$

    $\frac{a^6}{9b^{10}}$

    $\frac{9b^7}{a^6}$

29. Simplify the expression $\frac{(5x^{-2}y^3)^0 \cdot (x^2y^{-1})^3}{x^{-4}y^2}$. Assume $x \ne 0$ and $y \ne 0$.

    $x^2 y^{-1}$

    $\frac{x^{10}}{y^5}$

    $\frac{y^5}{x^{10}}$

    $x^2 y^5$

30. What is the value of $\left(\left(\frac{1}{3}\right)^{-2}\right)^{-1}$?

    $\frac{1}{9}$

    $-9$

    $3$

    $9$

31. Simplify $\frac{(2a^3b^{-2})^3}{4a^5b^{-7}}$. Assume $a \ne 0$ and $b \ne 0$.

    $2a^4b$

    $\frac{a^4}{2b}$

    $2a^4b^{-13}$

    $2a^4b^5$

32. Evaluate $(-2)^3 + 3^{-2} - (-4)^0$.

    $-\frac{80}{9}$

    $9$

    $-8$

    $-\frac{82}{9}$

33. If $2^{3x-1} = 16^2$, what is the value of $x$?

    $3/8$

    $4$

    $3$

    $2$

34. Simplify $\left(\left(\frac{m^2}{n^{-3}}\right)^{-1}\right)^2 \cdot m^5 n^{-2}$. Assume $m \ne 0$ and $n \ne 0$.

    $\frac{m}{n^8}$

    $m^{-9} n^{-8}$

    $\frac{n^8}{m}$

    $m n^8$

35. Evaluate $\left(\frac{3^{-1} + 2^{-1}}{(6^{-1})^0}\right)^{-1}$.

    $1$

    $\frac{6}{5}$

    $\frac{5}{6}$

    $\frac{1}{6}$

36. Simplify $\frac{5^2 \cdot 10^{-3}}{ (2 \cdot 5)^3 \cdot 5^{-5}}$.

    $5 \cdot 2^{-9}$

    $\frac{5}{128}$

    $\frac{1}{25}$

    $\frac{5}{64}$

37. Simplify $\frac{x^{2a} \cdot x^{b}}{x^{a-b}}$ where $x \ne 0$.

    $x^{a+b}$

    $x^{a}$

    $x^{a+2b}$

    $x^{3a}$

38. Simplify $( (-3x^{-2})^2 )^{-1}$. Assume $x \ne 0$.

    $\frac{x^4}{9}$

    $9x^4$

    $\frac{9}{x^4}$

    $-\frac{x^4}{9}$

39. Simplify $\left(\frac{4m^3 n^{-1}}{2m^2 n^0}\right)^3 \cdot m^{-5} n^4$. Assume $m \ne 0$ and $n \ne 0$.

    $\frac{8n}{m^2}$

    $\frac{8m^2}{n}$

    $8m^{-8}n^{-7}$

    $\frac{2n}{m^2}$

40. Evaluate $\left(\frac{(-1)^5 \cdot 2^3}{4^{-1}}\right)^0 + (-3)^{-2}$.

    $\frac{10}{9}$

    $1$

    $-\frac{1}{9}$

    $\frac{8}{9}$

41. Simplify $\frac{(ab^2)^{-3} \cdot (a^{-2}b)^2}{(a^3b^{-1})^{-1}}$. Assume $a \ne 0$ and $b \ne 0$.

    $a^{-10} b^{-3}$

    $\frac{b^5}{a^4}$

    $a^4 b^5$

    $\frac{1}{a^4b^5}$

42. What is the equivalent expression for $(2x^a y^b)^c \cdot (x^2 y^{-1})^{-2}$?

    $2^c x^{ac-4} y^{bc-2}$

    $2^c x^{ac-4} y^{bc+2}$

    $2^c x^{ac+4} y^{bc-2}$

    $2x^{ac-4}y^{bc+2}$

43. Evaluate $\left(-\frac{1}{2}\right)^3 \cdot (2^{-2})^{-1} \cdot 4^2$.

    $-16$

    $-4$

    $-8$

    $8$

44. Simplify $\frac{12a^0 b^{-5} (a^2b^3)^2}{(2a^{-1}b)^3}$. Assume $a \ne 0$ and $b \ne 0$.

    $\frac{3a}{2b^2}$

    $\frac{3a^7b^2}{2}$

    $\frac{3a^7}{2b^2}$

    $\frac{3}{2} a^7 b^{-8}$

45. Evaluate $(0.25)^{-2} \cdot 8^0 \cdot \frac{2^5}{4^{-1}}$.

    $4096$

    $1024$

    $512$

    $2048$