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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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