Laws of exponents Quiz - ICSE Class 7 Mathematics

Free practice quiz: Laws of exponents (ICSE Class 7 Mathematics). 51 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 7 Mathematics practice quiz has 51 multiple-choice questions on Laws of exponents, and 51 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Simplify: $(7^5 \times 7^3) / 7^4$

   1. $7^2$
   2. $7^4$
   3. $7^8$
   4. $7^{15}$
   Show answer

   Answer: B. $7^4$

   Using the law of exponents $a^m \times a^n = a^{m+n}$ and $a^m / a^n = a^{m-n}$, we have $(7^5 \times 7^3) / 7^4 = 7^{5+3} / 7^4 = 7^8 / 7^4 = 7^{8-4} = 7^4$.

2. Simplify: $a^3 \times a^5 \times a^2$

   1. $a^{10}$
   2. $a^{30}$
   3. $a^6$
   4. $a^{-2}$
   Show answer

   Answer: A. $a^{10}$

   Using the law of exponents $a^m \times a^n = a^{m+n}$, we have $a^3 \times a^5 \times a^2 = a^{3+5+2} = a^{10}$.

3. Evaluate: $(6^2)^3 / 6^4$

   1. $6^2$
   2. $6^3$
   3. $6^8$
   4. $6^{-2}$
   Show answer

   Answer: A. $6^2$

   Using the laws of exponents, $(6^2)^3 / 6^4 = 6^{2 imes 3} / 6^4 = 6^6 / 6^4 = 6^{6-4} = 6^2$.

4. Simplify: $9^5 / 9^5$

   1. $9^0$
   2. 1
   3. $9^{25}$
   4. 0
   Show answer

   Answer: A. $9^0$

   Using the law of exponents $a^m / a^n = a^{m-n}$, we have $9^5 / 9^5 = 9^{5-5} = 9^0$. Since any non-zero number raised to the power of 0 is 1, $9^0 = 1$.

5. Simplify: $(4^{-2})^3 / 4^{-5}$

   1. $4^{-11}$
   2. $4^{-1}$
   3. $4^1$
   4. $4^{-2}$
   Show answer

   Answer: B. $4^{-1}$

   Using the laws of exponents, $(4^{-2})^3 / 4^{-5} = 4^{-2 imes 3} / 4^{-5} = 4^{-6} / 4^{-5} = 4^{-6 - (-5)} = 4^{-6+5} = 4^{-1}$.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the value of $(3^{-2})^3$?
2. If $2^x = 128$, then what is the value of $x$?
3. Evaluate: $5^0 + 10^0 + 15^0$
4. Simplify: $(2^3)^4 / 2^{10}$
5. If $4^x = 256$, what is the value of $x$?
6. Calculate: $100^{-1} \times 10^2$
7. Which of the following is equivalent to $3^2 \times 3^3$?
8. Simplify: $5^7 / 5^4$
9. What is the value of $27^{1/3}$?
10. If $5^x = 625$, find $x$.
11. Evaluate: $(-2)^3 imes (-2)^2$
12. Simplify: $(3^4)^2$
13. What is $1 / 81$ expressed as a power of 3?
14. Calculate: $10^3 / 10^5$
15. Simplify: $(x^4 y^2)^3$
16. What is the value of $81^{3/4}$?
17. Simplify: $m^5 \times m^{-2} \times m^3$
18. If $10^x = 0.001$, what is the value of $x$?
19. Which of the following is equal to $5^{-3}$?
20. Simplify: $(x^3 y^{-2}) / (x^{-1} y^4)$
21. If $3^x = 1/243$, what is the value of $x$?
22. Calculate: $25^{1/2} imes 2^3$
23. Simplify: $y^7 / y^{-3}$
24. What is the value of $(1/2)^{-3}$?
25. If $a^m = 1$ and $a eq 0$, what is the value of $m$?
26. Simplify: $4^2 imes 4^{-5} imes 4^3$
27. What is $64^{1/2}$?
28. If $x^3 = 125$, what is the value of $x$?
29. Calculate: $(-3)^2 imes (-3)^{-4}$
30. What is the value of $(10^3)^0$?
31. Simplify: $7^8 / 7^3$
32. If $2^x = 1/16$, what is the value of $x$?
33. Evaluate: $(3/4)^2$
34. Simplify: $5^{-3} imes 5^7$
35. What is the value of $125^{2/3}$?
36. Calculate: $1000^{1/3}$
37. Which of the following is equivalent to $1/x^7$?
38. If $5^m = 5^2 imes 5^3$, find $m$.
39. Calculate: $3^2 imes 5^2$
40. What is the value of $(2^3)^4$?
41. Simplify: $x^9 / x^3$
42. If $10^x = 10000$, find $x$.
43. Calculate: $81^{3/4}$
44. Simplify: $(m^3)^2 imes m^4$
45. What is the value of $(2/3)^{-2}$?
46. If $4^a = 64$ and $3^b = 9$, find $a imes b$.

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