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Page 1
QUESTIONS
1. Simplify:
a. (4)
3
b. (3)
4
c. (5)
4
d. (7)
3
2. Simplify:
a. (2)
-3
b. (1)
-10
c. (6)
-2
d. (8)
-3
3. Simplify and write the answer in positive exponential form
a. (?? )
?? ÷ (?? )
??
b. (?? -?? × ?? -?? ) ÷ ?? ??
c. (?? -?? × ?? ?? ) ÷ (?? )
??
d. (?? ?? + ?? -?? + ?? -?? +?? -?? )
??
4. Simplify:
a. ?? ?? × ?? ?? × ?? ??
b. ?? ?? × ?? ?? × ?? ??
c. (
?? ?? )
?? × (
?? ?? )
?? × (
?? ?? )
-??
d. (
?? ?? )
?? × (
?? ?? )
?? × ????
??
5. Simplify: (-?? )
-?? × (-?? )
??
6. Simplify: [(-?? )
?? × (-?? )
?? ] ÷ (?? )
??
7. Find the value of ?? if , (?? )
?? = (???? )
??
8. Write (?????? )
-?? in the exponential form as base 5.
9. Simplify: [(-
?? ?? )
?? ]
??
10. Find the value of ?? if , (
?? ?? )
?? =
??????
??????
11. Find the value of
?? ?? if , (
?? ?? )
?? × (
?? ????
)
-?? =
?? ??
12. Simplify: (?? )
-?? × (?? )
-?? × ?????? × (?? )
??
13. Simplify: (?? -?? + ?? -?? ) ÷ (?? + ?? )
14. Simplify: (?? -?? × ?? -?? ) ÷ ?? -??
15. Simplify: (?? -?? + ????
?? ) ÷ (?? )
-??
16. Find the value of (???? × ?? ?? ), if ?? = ?? .
17. If (?? )
-?? =
?? (?? )
????
, then find the value of x.
18. Simplify: ?? ?? × ?? -?? × ?? ?? × ?? -????
Page 2
QUESTIONS
1. Simplify:
a. (4)
3
b. (3)
4
c. (5)
4
d. (7)
3
2. Simplify:
a. (2)
-3
b. (1)
-10
c. (6)
-2
d. (8)
-3
3. Simplify and write the answer in positive exponential form
a. (?? )
?? ÷ (?? )
??
b. (?? -?? × ?? -?? ) ÷ ?? ??
c. (?? -?? × ?? ?? ) ÷ (?? )
??
d. (?? ?? + ?? -?? + ?? -?? +?? -?? )
??
4. Simplify:
a. ?? ?? × ?? ?? × ?? ??
b. ?? ?? × ?? ?? × ?? ??
c. (
?? ?? )
?? × (
?? ?? )
?? × (
?? ?? )
-??
d. (
?? ?? )
?? × (
?? ?? )
?? × ????
??
5. Simplify: (-?? )
-?? × (-?? )
??
6. Simplify: [(-?? )
?? × (-?? )
?? ] ÷ (?? )
??
7. Find the value of ?? if , (?? )
?? = (???? )
??
8. Write (?????? )
-?? in the exponential form as base 5.
9. Simplify: [(-
?? ?? )
?? ]
??
10. Find the value of ?? if , (
?? ?? )
?? =
??????
??????
11. Find the value of
?? ?? if , (
?? ?? )
?? × (
?? ????
)
-?? =
?? ??
12. Simplify: (?? )
-?? × (?? )
-?? × ?????? × (?? )
??
13. Simplify: (?? -?? + ?? -?? ) ÷ (?? + ?? )
14. Simplify: (?? -?? × ?? -?? ) ÷ ?? -??
15. Simplify: (?? -?? + ????
?? ) ÷ (?? )
-??
16. Find the value of (???? × ?? ?? ), if ?? = ?? .
17. If (?? )
-?? =
?? (?? )
????
, then find the value of x.
18. Simplify: ?? ?? × ?? -?? × ?? ?? × ?? -????
19. If ?? ?? × ??????
?? = (???? )
?? ,then find the value of ?? .
20. If ?? ?? ÷ ?? ????
=
?? ?? , then find the value of ?? .
21. If (?? ?? × ?? -?? )
?? = ?????? ,then find the value of ?? .
22. Write 0.0081 in the standard form.
23. Write 1/10000000 in the standard form.
24. Write 4050000 in the standard form.
25. If (?? )
????
= ?????? , then find the value of x.
26. Find the value of x if ????
?? × ????
?? = (?? )
?? .
27. Find the value of (?? ?? × ?? ?? ) ÷ ???? if ?? = ?? ?????? ?? = ?? .
28. Simplify: (v?? )
?? ÷ (v?? )
??
29. Write ?? . ?????? × ????
-?? in general form.
30. Write ?? . ?????????? × ????
?? in general form.
31. If ?? = (
?? ?? )
?? × (
?? ?? )
?? , them find the value of ?? ?? .
32. Simplify: (v ?? )
?? + ?? ?? + ?? ?? + ?? ?? .
33. Find the value of (
?? ????
)
-?? /?? .
34. Find the value of (?????? )
-?? /?? .
35. Simplify: v ?? × (?? )
?? ??
36. If ?? ?? =
?? ????
, then find the value of x.
37. Simplify: (???? )
?? ?? × (???? )
?? ?? .
38. Find the value of [?? ?? + ?? ?? + ????
?? ]
?? ?? .
39. Simplify: (?? )
?? ?? -?? ?? . (?? )
?? ?? -?? ?? . (?? )
?? ?? -?? ?? .
40. Simplify:
(?? )
?? +?? .(?? )
?? +?? .(?? )
?? +?? (?? )
?? .(?? )
?? .(?? )
??
41. Find the value of ?? - v?? if v ?? = ?? . ??????
42. Find the value of [(?? )
?? + (?? )
?? + (?? )
?? ]
?? ??
43. Simplify:
v
v
v ?? ?? ??
44. Simplify:
v
v?? ????
?? ??
45. If (
v?? ?? )
?? = ?? - (
?? ?? )
?? , then find the value of ?? .
Page 3
QUESTIONS
1. Simplify:
a. (4)
3
b. (3)
4
c. (5)
4
d. (7)
3
2. Simplify:
a. (2)
-3
b. (1)
-10
c. (6)
-2
d. (8)
-3
3. Simplify and write the answer in positive exponential form
a. (?? )
?? ÷ (?? )
??
b. (?? -?? × ?? -?? ) ÷ ?? ??
c. (?? -?? × ?? ?? ) ÷ (?? )
??
d. (?? ?? + ?? -?? + ?? -?? +?? -?? )
??
4. Simplify:
a. ?? ?? × ?? ?? × ?? ??
b. ?? ?? × ?? ?? × ?? ??
c. (
?? ?? )
?? × (
?? ?? )
?? × (
?? ?? )
-??
d. (
?? ?? )
?? × (
?? ?? )
?? × ????
??
5. Simplify: (-?? )
-?? × (-?? )
??
6. Simplify: [(-?? )
?? × (-?? )
?? ] ÷ (?? )
??
7. Find the value of ?? if , (?? )
?? = (???? )
??
8. Write (?????? )
-?? in the exponential form as base 5.
9. Simplify: [(-
?? ?? )
?? ]
??
10. Find the value of ?? if , (
?? ?? )
?? =
??????
??????
11. Find the value of
?? ?? if , (
?? ?? )
?? × (
?? ????
)
-?? =
?? ??
12. Simplify: (?? )
-?? × (?? )
-?? × ?????? × (?? )
??
13. Simplify: (?? -?? + ?? -?? ) ÷ (?? + ?? )
14. Simplify: (?? -?? × ?? -?? ) ÷ ?? -??
15. Simplify: (?? -?? + ????
?? ) ÷ (?? )
-??
16. Find the value of (???? × ?? ?? ), if ?? = ?? .
17. If (?? )
-?? =
?? (?? )
????
, then find the value of x.
18. Simplify: ?? ?? × ?? -?? × ?? ?? × ?? -????
19. If ?? ?? × ??????
?? = (???? )
?? ,then find the value of ?? .
20. If ?? ?? ÷ ?? ????
=
?? ?? , then find the value of ?? .
21. If (?? ?? × ?? -?? )
?? = ?????? ,then find the value of ?? .
22. Write 0.0081 in the standard form.
23. Write 1/10000000 in the standard form.
24. Write 4050000 in the standard form.
25. If (?? )
????
= ?????? , then find the value of x.
26. Find the value of x if ????
?? × ????
?? = (?? )
?? .
27. Find the value of (?? ?? × ?? ?? ) ÷ ???? if ?? = ?? ?????? ?? = ?? .
28. Simplify: (v?? )
?? ÷ (v?? )
??
29. Write ?? . ?????? × ????
-?? in general form.
30. Write ?? . ?????????? × ????
?? in general form.
31. If ?? = (
?? ?? )
?? × (
?? ?? )
?? , them find the value of ?? ?? .
32. Simplify: (v ?? )
?? + ?? ?? + ?? ?? + ?? ?? .
33. Find the value of (
?? ????
)
-?? /?? .
34. Find the value of (?????? )
-?? /?? .
35. Simplify: v ?? × (?? )
?? ??
36. If ?? ?? =
?? ????
, then find the value of x.
37. Simplify: (???? )
?? ?? × (???? )
?? ?? .
38. Find the value of [?? ?? + ?? ?? + ????
?? ]
?? ?? .
39. Simplify: (?? )
?? ?? -?? ?? . (?? )
?? ?? -?? ?? . (?? )
?? ?? -?? ?? .
40. Simplify:
(?? )
?? +?? .(?? )
?? +?? .(?? )
?? +?? (?? )
?? .(?? )
?? .(?? )
??
41. Find the value of ?? - v?? if v ?? = ?? . ??????
42. Find the value of [(?? )
?? + (?? )
?? + (?? )
?? ]
?? ??
43. Simplify:
v
v
v ?? ?? ??
44. Simplify:
v
v?? ????
?? ??
45. If (
v?? ?? )
?? = ?? - (
?? ?? )
?? , then find the value of ?? .
ANSWERS
Question
No.
Answer Question No. Answer
1.
a. 64 b. 81
c. 625 d. 343
19.
20.
21.
22.
?? = ??
?? = ??
?? = ????
?? . ?? × ????
-??
2.
a.
?? ?? b. 1
c.
?? ????
d.
?? ??????
23.
24.
25.
26.
27.
?? × ????
-??
?? . ???? × ????
??
?? = ??
?? = ????
12
3.
a. 4 b.
?? ?? ??
c.
?? ?? ?? d. 1
28.
29.
30.
31.
5
0.0009432
32
?? ??
4.
a. 1800 b. 4900
c.
?? ????
d.
?? ??
32.
33.
34.
35.
18
9
?? ????
4
5.
-
????
??????
36. -
?? ??
6. -
????????
?? 37. ????
7.
?? = ????
38. 12
8.
(?? )
-??
39. 1
9.
????
??????
40. (?? )
?? +?? +??
10. ?? = ?? 41. ?? . ??????
11.
?? ??
42. 2
12.
?? ??????
43.
(?? )
?? ????
13.
?? ????
44. ?? ??
14. 1 45. ?? = ??
15. 5
16. 36
17.
?? = ??
18.
?? ????
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FAQs on Mental Maths Questions and Answers: Exponents and Powers - Mental Mathematics for Class 8
| 1. What is an exponent in mathematics? |  |
Ans. An exponent in mathematics is a small number placed to the right and above another number, indicating how many times the base number should be multiplied by itself.
| 2. How do you calculate a number raised to an exponent? | |
Ans. To calculate a number raised to an exponent, you simply multiply the base number by itself the number of times indicated by the exponent.
| 3. What is the difference between an exponent and a power in mathematics? | |
Ans. An exponent is the small number indicating how many times to multiply the base number, while the power is the result of raising a number to an exponent.
| 4. Can exponents be negative numbers? | |
Ans. Yes, exponents can be negative numbers. A negative exponent indicates the reciprocal of the base number raised to the positive exponent.
| 5. How do you simplify expressions with exponents and powers? | |
Ans. To simplify expressions with exponents and powers, follow the rules of exponents such as multiplying exponents when the base numbers are the same, or dividing exponents when subtracting.
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Dec 22, 2024 Last updated |
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