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Page 1
EXPONENTS AND POWERS
Points to Remember
Recall that we may write 3×3×3×3 as 3
4
and read it as three raise to the power
four. In 3
4
, we call 3 as base and 4 as exponent. Similarly, when an integer ‘a’ is
multiplied ‘n’ times the result is expressed as a
n
. Here ‘a’ is called the base and ‘n’
is called as exponent.
? LAWS OF EXPONENTS:
(i). a
m
× a
n
= a
m + n
(ii).
?? ?? ?? ?? = a
m - n
(iii). ( a
m
)
n
= a
m x n
(iv). a
m
× b
m
= (ab)
m
(v). a
m
÷ b
m
= (
?? ?? )
m
(vi). a
- m
=
?? ?? ??
? Further we recall that
(i). a
0
= 1
(ii). (- 1)
even number
= 1
(iii). (- 1)
odd number
= - 1
? STANDARD FORM:
When a number is expressed as a decimal between 1.0 and 10.0 multiplied by a
power of 10 is called its standard form. Thus A × 10
n
is the standard form where
1 = A< 10, n is an integer. For example, a number 2806196 can be expressed in
standard form as 2.806196 × 10
6
Questions:
1. What is the base and exponent of 10
– 3
?
2. Write in exponential form: (-2) × (-2) × (-2) × (-2) × (-2) × (-2).
Page 2
EXPONENTS AND POWERS
Points to Remember
Recall that we may write 3×3×3×3 as 3
4
and read it as three raise to the power
four. In 3
4
, we call 3 as base and 4 as exponent. Similarly, when an integer ‘a’ is
multiplied ‘n’ times the result is expressed as a
n
. Here ‘a’ is called the base and ‘n’
is called as exponent.
? LAWS OF EXPONENTS:
(i). a
m
× a
n
= a
m + n
(ii).
?? ?? ?? ?? = a
m - n
(iii). ( a
m
)
n
= a
m x n
(iv). a
m
× b
m
= (ab)
m
(v). a
m
÷ b
m
= (
?? ?? )
m
(vi). a
- m
=
?? ?? ??
? Further we recall that
(i). a
0
= 1
(ii). (- 1)
even number
= 1
(iii). (- 1)
odd number
= - 1
? STANDARD FORM:
When a number is expressed as a decimal between 1.0 and 10.0 multiplied by a
power of 10 is called its standard form. Thus A × 10
n
is the standard form where
1 = A< 10, n is an integer. For example, a number 2806196 can be expressed in
standard form as 2.806196 × 10
6
Questions:
1. What is the base and exponent of 10
– 3
?
2. Write in exponential form: (-2) × (-2) × (-2) × (-2) × (-2) × (-2).
3. Write in exponential form a × b ×a × b × b.
4. Find the value of (-2)
2
× (-2)
3
5. If 4
3
= 4
x
, then find x.
6. Express 64 x 27 in exponential form.
7. Express 2000000 in standard form.
8. What is usual form of 3.469 ×
10
6
?
9. Simplify: (2
-1
× 3
- 1
× 4
-1
)
2
.
10. Change into negative exponent (
?? ?? )
?? .
11. Simplify: (1234)
0
× 2
3
× x
2
× y.
12. Find the value of 9
0
× 99
0
× 125
0
× 256
0
.
13. Find the value of (a
0
+ b
0
) × (a
0
- b
0
).
14. Find the reciprocal of
?? ????
.
15. Simplify: 2
3
× 2
5
× 2
7
.
16. Simplify: (
?? ????
)
2
× (- 6)
3
17. Express
??????
??????
in exponential form.
18. If a
2
b
3
= a
2x
b
y
. Find x and y.
19. Simplify: (2p
3
)
3
÷ 3 (p
2
)
3
20. Find value of (???? )
-
?? ?? × (???? )
?? ??
21. Simplify:
?? ?? ?? ?? ?? ???? ?? ?? ?? ??
22. Find the value of ((???? )
?? ?? + (???? )
?? ?? )
.
23. Find the value of (-
?? ????
)
?? ??
24. Find the reciprocal of ( -
?? ?? )
2
Page 3
EXPONENTS AND POWERS
Points to Remember
Recall that we may write 3×3×3×3 as 3
4
and read it as three raise to the power
four. In 3
4
, we call 3 as base and 4 as exponent. Similarly, when an integer ‘a’ is
multiplied ‘n’ times the result is expressed as a
n
. Here ‘a’ is called the base and ‘n’
is called as exponent.
? LAWS OF EXPONENTS:
(i). a
m
× a
n
= a
m + n
(ii).
?? ?? ?? ?? = a
m - n
(iii). ( a
m
)
n
= a
m x n
(iv). a
m
× b
m
= (ab)
m
(v). a
m
÷ b
m
= (
?? ?? )
m
(vi). a
- m
=
?? ?? ??
? Further we recall that
(i). a
0
= 1
(ii). (- 1)
even number
= 1
(iii). (- 1)
odd number
= - 1
? STANDARD FORM:
When a number is expressed as a decimal between 1.0 and 10.0 multiplied by a
power of 10 is called its standard form. Thus A × 10
n
is the standard form where
1 = A< 10, n is an integer. For example, a number 2806196 can be expressed in
standard form as 2.806196 × 10
6
Questions:
1. What is the base and exponent of 10
– 3
?
2. Write in exponential form: (-2) × (-2) × (-2) × (-2) × (-2) × (-2).
3. Write in exponential form a × b ×a × b × b.
4. Find the value of (-2)
2
× (-2)
3
5. If 4
3
= 4
x
, then find x.
6. Express 64 x 27 in exponential form.
7. Express 2000000 in standard form.
8. What is usual form of 3.469 ×
10
6
?
9. Simplify: (2
-1
× 3
- 1
× 4
-1
)
2
.
10. Change into negative exponent (
?? ?? )
?? .
11. Simplify: (1234)
0
× 2
3
× x
2
× y.
12. Find the value of 9
0
× 99
0
× 125
0
× 256
0
.
13. Find the value of (a
0
+ b
0
) × (a
0
- b
0
).
14. Find the reciprocal of
?? ????
.
15. Simplify: 2
3
× 2
5
× 2
7
.
16. Simplify: (
?? ????
)
2
× (- 6)
3
17. Express
??????
??????
in exponential form.
18. If a
2
b
3
= a
2x
b
y
. Find x and y.
19. Simplify: (2p
3
)
3
÷ 3 (p
2
)
3
20. Find value of (???? )
-
?? ?? × (???? )
?? ??
21. Simplify:
?? ?? ?? ?? ?? ???? ?? ?? ?? ??
22. Find the value of ((???? )
?? ?? + (???? )
?? ?? )
.
23. Find the value of (-
?? ????
)
?? ??
24. Find the reciprocal of ( -
?? ?? )
2
25. Express
??????
????
in exponential form.
26. Express
??????
??????
in exponential form.
27. Simplify: [(?? ?? ?? )
3/8
]
2
28. Simplify: (
?? ?? )
-?? × (
?? ?? )
?? × a
3
× b
3
29. What is usual form of 2.29 × 10
4
.
30. If (
??
?? )
2
× (
??
?? )
t
= 1, then find the value of t.
31. The speed of light is 300000000 m/s. Express it in standard form.
32. Change in to positive exponent (
?? ?? )
- ?? .
33. Change in to negative exponent ( ?? ?? )
?? .
34. If ?? ????
= 64, then find the value of x.
35. Find the value of x if ?? ????
× ?? ?? = ?? ?? .
36. What number is obtained from expanded form
5 × ????
?? + 2 × ????
?? + 5× ????
?? + 2 × ????
?? + ????
??
37. The distance of moon from earth is 384000 km, express it in standard
form.
38. If
?? ?? = (
?? ?? )
?? -(
?? ?? )
?? , then find the value of
?? ?? .
39. Find the value of ( ?? -?? - ?? -?? ) × ????
?? .
40. If ?? ?? × ?? ?? = 64 ×81, then find the value of x + y.
41. What is the standard form of the number 2467895?
42. Find the value of x: ( -
?? ?? )
????
÷ (-
?? ?? )
?? = (-
?? ?? )
???? + ??
43. Simplify and express in exponential form:
{ ( ?? ?? )
?? × ?? ?? } ÷{?? ?? × ?? ?? }
Page 4
EXPONENTS AND POWERS
Points to Remember
Recall that we may write 3×3×3×3 as 3
4
and read it as three raise to the power
four. In 3
4
, we call 3 as base and 4 as exponent. Similarly, when an integer ‘a’ is
multiplied ‘n’ times the result is expressed as a
n
. Here ‘a’ is called the base and ‘n’
is called as exponent.
? LAWS OF EXPONENTS:
(i). a
m
× a
n
= a
m + n
(ii).
?? ?? ?? ?? = a
m - n
(iii). ( a
m
)
n
= a
m x n
(iv). a
m
× b
m
= (ab)
m
(v). a
m
÷ b
m
= (
?? ?? )
m
(vi). a
- m
=
?? ?? ??
? Further we recall that
(i). a
0
= 1
(ii). (- 1)
even number
= 1
(iii). (- 1)
odd number
= - 1
? STANDARD FORM:
When a number is expressed as a decimal between 1.0 and 10.0 multiplied by a
power of 10 is called its standard form. Thus A × 10
n
is the standard form where
1 = A< 10, n is an integer. For example, a number 2806196 can be expressed in
standard form as 2.806196 × 10
6
Questions:
1. What is the base and exponent of 10
– 3
?
2. Write in exponential form: (-2) × (-2) × (-2) × (-2) × (-2) × (-2).
3. Write in exponential form a × b ×a × b × b.
4. Find the value of (-2)
2
× (-2)
3
5. If 4
3
= 4
x
, then find x.
6. Express 64 x 27 in exponential form.
7. Express 2000000 in standard form.
8. What is usual form of 3.469 ×
10
6
?
9. Simplify: (2
-1
× 3
- 1
× 4
-1
)
2
.
10. Change into negative exponent (
?? ?? )
?? .
11. Simplify: (1234)
0
× 2
3
× x
2
× y.
12. Find the value of 9
0
× 99
0
× 125
0
× 256
0
.
13. Find the value of (a
0
+ b
0
) × (a
0
- b
0
).
14. Find the reciprocal of
?? ????
.
15. Simplify: 2
3
× 2
5
× 2
7
.
16. Simplify: (
?? ????
)
2
× (- 6)
3
17. Express
??????
??????
in exponential form.
18. If a
2
b
3
= a
2x
b
y
. Find x and y.
19. Simplify: (2p
3
)
3
÷ 3 (p
2
)
3
20. Find value of (???? )
-
?? ?? × (???? )
?? ??
21. Simplify:
?? ?? ?? ?? ?? ???? ?? ?? ?? ??
22. Find the value of ((???? )
?? ?? + (???? )
?? ?? )
.
23. Find the value of (-
?? ????
)
?? ??
24. Find the reciprocal of ( -
?? ?? )
2
25. Express
??????
????
in exponential form.
26. Express
??????
??????
in exponential form.
27. Simplify: [(?? ?? ?? )
3/8
]
2
28. Simplify: (
?? ?? )
-?? × (
?? ?? )
?? × a
3
× b
3
29. What is usual form of 2.29 × 10
4
.
30. If (
??
?? )
2
× (
??
?? )
t
= 1, then find the value of t.
31. The speed of light is 300000000 m/s. Express it in standard form.
32. Change in to positive exponent (
?? ?? )
- ?? .
33. Change in to negative exponent ( ?? ?? )
?? .
34. If ?? ????
= 64, then find the value of x.
35. Find the value of x if ?? ????
× ?? ?? = ?? ?? .
36. What number is obtained from expanded form
5 × ????
?? + 2 × ????
?? + 5× ????
?? + 2 × ????
?? + ????
??
37. The distance of moon from earth is 384000 km, express it in standard
form.
38. If
?? ?? = (
?? ?? )
?? -(
?? ?? )
?? , then find the value of
?? ?? .
39. Find the value of ( ?? -?? - ?? -?? ) × ????
?? .
40. If ?? ?? × ?? ?? = 64 ×81, then find the value of x + y.
41. What is the standard form of the number 2467895?
42. Find the value of x: ( -
?? ?? )
????
÷ (-
?? ?? )
?? = (-
?? ?? )
???? + ??
43. Simplify and express in exponential form:
{ ( ?? ?? )
?? × ?? ?? } ÷{?? ?? × ?? ?? }
44. What is the standard form of the number 0.0032456?
45. Simplify: ( ?? - ?? × ?? - ?? × ?? )
?? .
46. If ?? ????
= ??????
?? , find the value of x.
47. Find the value of x if, ( ?? ?? ÷ ?? - ?? )× ?? ????
= ?? ??
48. Simplify: (
?? ?? )
- ?? + (
?? ?? )
- ?? + (
?? ?? )
- ??
49. Find the reciprocal of (
?? ?? )
- ?? ÷ (
?? ?? )
- ?? .
50. Simplify:
(
?? ?? )
?? × (
?? ?? )
?? ?? ??
×(
?? ?? )
??
Page 5
EXPONENTS AND POWERS
Points to Remember
Recall that we may write 3×3×3×3 as 3
4
and read it as three raise to the power
four. In 3
4
, we call 3 as base and 4 as exponent. Similarly, when an integer ‘a’ is
multiplied ‘n’ times the result is expressed as a
n
. Here ‘a’ is called the base and ‘n’
is called as exponent.
? LAWS OF EXPONENTS:
(i). a
m
× a
n
= a
m + n
(ii).
?? ?? ?? ?? = a
m - n
(iii). ( a
m
)
n
= a
m x n
(iv). a
m
× b
m
= (ab)
m
(v). a
m
÷ b
m
= (
?? ?? )
m
(vi). a
- m
=
?? ?? ??
? Further we recall that
(i). a
0
= 1
(ii). (- 1)
even number
= 1
(iii). (- 1)
odd number
= - 1
? STANDARD FORM:
When a number is expressed as a decimal between 1.0 and 10.0 multiplied by a
power of 10 is called its standard form. Thus A × 10
n
is the standard form where
1 = A< 10, n is an integer. For example, a number 2806196 can be expressed in
standard form as 2.806196 × 10
6
Questions:
1. What is the base and exponent of 10
– 3
?
2. Write in exponential form: (-2) × (-2) × (-2) × (-2) × (-2) × (-2).
3. Write in exponential form a × b ×a × b × b.
4. Find the value of (-2)
2
× (-2)
3
5. If 4
3
= 4
x
, then find x.
6. Express 64 x 27 in exponential form.
7. Express 2000000 in standard form.
8. What is usual form of 3.469 ×
10
6
?
9. Simplify: (2
-1
× 3
- 1
× 4
-1
)
2
.
10. Change into negative exponent (
?? ?? )
?? .
11. Simplify: (1234)
0
× 2
3
× x
2
× y.
12. Find the value of 9
0
× 99
0
× 125
0
× 256
0
.
13. Find the value of (a
0
+ b
0
) × (a
0
- b
0
).
14. Find the reciprocal of
?? ????
.
15. Simplify: 2
3
× 2
5
× 2
7
.
16. Simplify: (
?? ????
)
2
× (- 6)
3
17. Express
??????
??????
in exponential form.
18. If a
2
b
3
= a
2x
b
y
. Find x and y.
19. Simplify: (2p
3
)
3
÷ 3 (p
2
)
3
20. Find value of (???? )
-
?? ?? × (???? )
?? ??
21. Simplify:
?? ?? ?? ?? ?? ???? ?? ?? ?? ??
22. Find the value of ((???? )
?? ?? + (???? )
?? ?? )
.
23. Find the value of (-
?? ????
)
?? ??
24. Find the reciprocal of ( -
?? ?? )
2
25. Express
??????
????
in exponential form.
26. Express
??????
??????
in exponential form.
27. Simplify: [(?? ?? ?? )
3/8
]
2
28. Simplify: (
?? ?? )
-?? × (
?? ?? )
?? × a
3
× b
3
29. What is usual form of 2.29 × 10
4
.
30. If (
??
?? )
2
× (
??
?? )
t
= 1, then find the value of t.
31. The speed of light is 300000000 m/s. Express it in standard form.
32. Change in to positive exponent (
?? ?? )
- ?? .
33. Change in to negative exponent ( ?? ?? )
?? .
34. If ?? ????
= 64, then find the value of x.
35. Find the value of x if ?? ????
× ?? ?? = ?? ?? .
36. What number is obtained from expanded form
5 × ????
?? + 2 × ????
?? + 5× ????
?? + 2 × ????
?? + ????
??
37. The distance of moon from earth is 384000 km, express it in standard
form.
38. If
?? ?? = (
?? ?? )
?? -(
?? ?? )
?? , then find the value of
?? ?? .
39. Find the value of ( ?? -?? - ?? -?? ) × ????
?? .
40. If ?? ?? × ?? ?? = 64 ×81, then find the value of x + y.
41. What is the standard form of the number 2467895?
42. Find the value of x: ( -
?? ?? )
????
÷ (-
?? ?? )
?? = (-
?? ?? )
???? + ??
43. Simplify and express in exponential form:
{ ( ?? ?? )
?? × ?? ?? } ÷{?? ?? × ?? ?? }
44. What is the standard form of the number 0.0032456?
45. Simplify: ( ?? - ?? × ?? - ?? × ?? )
?? .
46. If ?? ????
= ??????
?? , find the value of x.
47. Find the value of x if, ( ?? ?? ÷ ?? - ?? )× ?? ????
= ?? ??
48. Simplify: (
?? ?? )
- ?? + (
?? ?? )
- ?? + (
?? ?? )
- ??
49. Find the reciprocal of (
?? ?? )
- ?? ÷ (
?? ?? )
- ?? .
50. Simplify:
(
?? ?? )
?? × (
?? ?? )
?? ?? ??
×(
?? ?? )
??
ANSWERS
1 Base= 10, Exponent = - 3 26
(
?? ?? )
?? or
?? ?? ?? ??
2 (-?? )
?? 27 ?? ?? /??
3 ?? ?? ?? ??
28 ?? ??
4 -???? 29 22900
5 x = 3 30 ?? = -??
6 ?? ?? ?? ?? 31 ?? . ?? × ????
?? m/s
7 ?? × ????
?? 32
(
?? ?? )
??
8 3469000 33
(
?? ?? )
-????
9
?? ??????
34
?? =
?? ??
10
(
?? ?? )
-??
35 ?? = ??
11 ?? ?? ?? ?? 36 52521
12 1 37 ?? . ???? × ????
?? km
13 0 38
-
????
????
14
????
??
39
-
?? ????
15 ?? ????
40 ?? + ?? = 10
16
-
?? ??
41 ?? . ???????????? × ????
??
17 ?? ?? ?? ??
42 ?? = ??
18 ?? = ?? , ?? = ?? 43 ?? ??
19
?? ?? ?? ??
44 ?? . ???????? × ????
-??
20
?? ??
45
?? ??
21
?? ?? ?? ??
46 ?? = ??
22 100 47 ?? = ????
23
?? ????
48 29
24 9 49
????
??
25 ?? ?? ?? ??
50
?? ????
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Whether you're a beginner or aiming for advanced proficiency, Mental Maths Questions and Answers: Exponents and Power Notes on EduRev are your ultimate resource for success.
Mental Maths Questions and Answers: Exponents and Power Class 7
The "Mental Maths Questions and Answers: Exponents and Power Class 7 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 7 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Mental Maths Questions and Answers: Exponents and Power on the App
Students of Class 7 can study Mental Maths Questions and Answers: Exponents and Power alongwith tests & analysis from the EduRev app,
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The content of Mental Maths Questions and Answers: Exponents and Power is prepared as per the latest Class 7 syllabus.
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