Class 8 Maths Notes for Exponents And Power

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CLASS 8
MATHS

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EXPONENTS AND POWERS
I IMPORTANT CONCEPTS
 X³ here X means base and 3 is its exponent , it is read as X raised to power 3
 some laws of exponent
 𝑥 𝑚 X 𝑥 𝑛 = 𝑥 𝑚 +𝑛
 𝑥 𝑚 ÷ 𝑥 𝑛 = 𝑥 𝑚 −𝑛
 (𝑥 𝑚 )𝑛 = 𝑥 𝑚𝑛
 𝑥 𝑚 𝑋 𝑦 𝑚 = (𝑥𝑦)𝑚
𝑥𝑚 𝑥 𝑚
 =
𝑦𝑚 𝑦
1
 𝑥 −1
=
𝑥
 𝑥 =10

 −1 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑜 . = 1
 −1 𝑎𝑛 𝑜𝑑𝑑 𝑛𝑜 . = −1
 A number is said to be in standard form , if it is expressed as the product of a no. between 1 to 10 and
the integral power of 10.
 14800000000= 1.48 x 1010
0.0000056 = 5.6 𝑋10−6

II Some iilustrations/ examples
 MCQs
−7 −1
1) is equal to
5
5 −5 7 −7
𝑎) 7 b) 7 c)5 d) 5
−7 −1 −5
𝑆𝑜𝑙𝑛. = b) 7 ( ans. b)
5
3 8
2)9 ÷ 9 =
a)95 b)9−5 𝑐)−95 𝑑)−9−5
3−8 −5
Soln.9 =9 (ans. b)
−1
3) Cube of 2 is
−1 1 1 1
a) 8 b) 16 c) 8 d) 4
−1 3 −1 −1 −1 −1
Soln. 2 = 2 = ) 8 (ans . a)
2 2
4) The value of p ,for which 77 ÷ 7−𝑝 = 710 is
a)1 b)2 c)3 d) 4
7−(−𝑝)
Soln. 7 = 710
7+p = 10 (bases are same so powers are equal)
P=3 (ans . c)
SHORT ANSWER TYPE QUESTIONS
1 −2 1 −2 1 −2
1) simplify: + 2 + 3
4
Sol. 4 + 2 + 32 = 16 + 4 + 9 = 29
2 2

23 𝑋 27
2)simplify :31 𝑋 4 6
23+7 210 210 −12 2−2 1 1
Soln. = 212 𝑋 3 = = 3 = 3𝑋22 =12
22 6 𝑋 3 3
3)Find the value of m for which 5𝑚 ÷ 5−3 = 55

50

Soln. 5𝑚 −(−3) = 55
=>5𝑚 +3 = 55
since bases are equal , therefore exponents will also be equal
m+3 = 5 => m= 5-3 = 2
4) Find the multiplicative inverse of (7−2 ÷ 90−1 )
1 1
Soln.72 ÷ 90
1 1
= 49 ÷ 90
1
= 49 𝑋 90
90
= 49
49
the multiplicative inverse of (7−2 ÷ 90−1 ) = 90
LONG ANSWER TYPE QUESTIONS
5𝑚 𝑋 53 𝑋 5−2
1) If = 512 find m
5−5
Soln.5𝑚 × 53 × 5−2 × 55 = 512
=5𝑚 +3−2+5 = 512
=5𝑚 +6 = 512
=> m+6 = 12 [ as bases are same]
=> m = 12-6 = 6
1 45 1 −60 1 28 1 −43
2) Simplify ; × − ×
5 5 5 5
1 45−60 1 28−43
Soln. −
5 5
1 −15 1 −15
= −
5 5
= 515 − 515 = 0
 CASE STUDY BASED QUESTIONS
A child was reading about cells of which living things are made of , while reading he finds
the size of red blood cell to be 0.000007m that of a plant cell size of 0.0000129m.
Based on above situation answer the following questions
a) Express the size of both cells in standard form
b) Can we see the cells by naked eyes?
c) Compare the sizes of cell?
Soln.
a) size of red blood cell is 0.000007m= 7× 10−6 𝑚
size of a plant cell is is 0.0000129m = 1.29 × 10−5 𝑚
b) no, as minimum size which we can observe is mm.
7X 10 −6 𝑚 7 𝑋10 −6+5 7 𝑋10 −1 7 7 7
c) comparison of their sizes = 1.29 X10 −5 𝑚 = = = = 1.29𝑋 10 = 12.9 = 13
1.29 1.29
1
=2 approx i.e the size of red blood cell is half the size of plant cell.
III QUESTIONS FOR PRACTICE
MCQs
1) 𝑥 𝑚 𝑛 is expressed as
a)𝑥 𝑚 +𝑛 b)𝑥 𝑚𝑛 c)𝑥 𝑚 −𝑛 d)𝑥 𝑚 ÷𝑛
𝑥 𝑚
2) 𝑦 is expressed as

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a)(𝑥 − 𝑦)𝑚 b)(𝑥 + 𝑦)𝑚 c)𝑥 𝑚 𝑋𝑦 −𝑚 d)all are incorrect
1 −2
3) What is the value of 2
1 1 c)-4 d)4
a)−4 b)4
4)What is the value of 2 + 70 × 100
0

a)72 b)9 c)1 d)2

5) 2−1 + 3−1 + 4−1 0 equals to
a)2+3+4 b)1+1+1 1 1 1 d)1
c)2 + 3 + 4
6) In 5𝑛 , n is known as
a) base b) exponent c)constant d)number
7) The standard form for 0.000064
a)64× 104 b) 64× 10−4 c) 6.4× 10−5 d) 6.4× 105
8) What is the value of 4.05 X 106 in usual form ?
a)40500 b)405000 c)0.0000045 d)4050000
2
9) What is value of 2 × 3 ?
a)12 b)18 c)36 d)8
1 0
10) What is value of 10
a)1 b)10 c)0 1
d)10

SHORT ANSWER TYPE QUESTIONS
1) Simplify :3−7 ÷ 3−10 × 3−5
2) Find the value of : ( 30 + 4−1 )× 22
3) Find the value of : ( 3−1 × 4−1 )÷2−2
8−1 × 53
4) Evaluate : 2−4
5) Find m so that (−3)𝑚 +1 × ( −3)5 = (−3)7
6) Simplify and express in exponential form : 25 ÷ 28 5 × 2−5
−1
1 −1 1 −1
7) Evaluate : −
3 4
8) Express following in usual form : a) 4.5 × 104 ,b) 3× 10−3
9) Express in standard form : a) 3080000 , b) 0.00067
5 4
10) Simplify and express in exponential form : −3 4 × 3

LONG ANSWER TYPE QUESTIONS
25 × t −4
1) Simplify :5−3 ×10 1 ×t −8
3−5 ×10 −5 ×125 1
2) Simplify : 5−7 ×6−5
2 2𝑥+6 2 3 2 𝑥+2
3) Find x : 5 × =
5 5
4) By what number should (−8)−3 be multiplied so that the product may be equal to −6−3 ?
4 4 13 2 7 3
5) Simplify : 13 × ×
7 4

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−3 −3 9 −2
6) By what number should be divided so that the quotient is 4 ?
2
CASE STUDY BASED QUESTIONS
1)In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness 0.016 mm.
a) What is the thickness of 5 books in cm?
b) What is the thickness of 5 paper sheets in mm?
c) What is the total thickness of the stack.

2)The distance between Sun and Earth is 1.496 X 1011 m and the distance between Earth and Moon is 3.84 X
108 𝑚 . During solar eclipse moon comes in between Earth and Sun .
a) 3.84 × 108 𝑚 = 384 × ___.
b)1.496 × 1011 = ___ × 108
c)Find the distance between Moon and Sun.

ANSWERS OF PRACTICE QUESTIONS
MCQs
1)b 2) c 3)d 4)d 5)d 6)b 7)c 8)d 9)c 10)c
SHORT ANSWER TYPE QUESTIONS
1 1 1
1)9 2)5 3) 3 4) 250 5) 1 6)220 7) -1 8)a) 45000 b)0.003
9)a)3.08× 106 𝑏)6.7 ×, 10−4 10)625
LONG ANSWER TYPE QUESTIONS
𝟔𝟐𝟓 𝒕𝟒 64 28 −3
1) 2)3125 3)-7 4)27 5)169 6) 2
2
CASE STUDY BASED QUESTION
1) a)10cm b)0.08mm c)1.0008× 102 mm
2) a)106 m b)1496 × 108 c)1492.16 × 108 m

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CLASS – VIII TOPIC: Exponents and powers MM -20
I Fill in the blanks : (10)
−7 −1
1. is equal to ___
5
2. −1 103 = ____
−5 −99
3. The multiplicative inverse of is ___
3
4. The standard form of 0.000064 is ___
−5 3
5. The value of × 7 3 = ___
7
1
6. expressed as power of 5 is ___
25
7. 108 × 10−10 = ___
3 −2
8. The value of is ___
2
9. 7 × 10−6 ___129 × 10−7 (< or >)
10. 50 + 60 = ___
II Short answer type questions : 5X2 =10
1 −2 1 −2 1 −2
1. simplify: + 2 + 3
4
2. Find the value of m for which 2𝑚 ÷ 2−2 = 25
3. Simplify :5−7 ÷ 5−10 × 5−5
2
1 −1 1 −1
4. Evaluate : −
3 4
5. Express following in usual form : a) 7.5 × 104 ,b) 2.3× 10−3

Long answer type questions (8)
2 2𝑥+6 2 3 2 𝑥+2
7) Find x : 5 𝑋 5 = 5
8) In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness 0.016 mm.
Find the total thickness of stack in standard form.

CLASS – VIII TOPIC: Exponents and powers MM -20
I Fill in the blanks : (10)
−7 −1
11. is equal to ___
5
12. −1 103 = ____
−5 −99
13. The multiplicative inverse of is ___
3
14. The standard form of 0.000064 is ___
−5 3
15. The value of × 7 3 = ___
7

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1
16. 25 expressed as power of 5 is ___
17. 108 𝑋10−10 = ___
3 −2
18. The value of is ___
2
19. 7 × 10 ___129 × 10−7 (< or >)
−6

20. 50 + 60 = ___
II Short answer type questions : 5X2 =10
1 −2 1 −2 1 −2
6. simplify: + 2 + 3
4
7. Find the value of m for which 2𝑚 ÷ 2−2 = 25
8. Simplify :5−7 ÷ 5−10 × 5−5
2
1 −1 1 −1
9. Evaluate : −
3 4
10. Express following in usual form : a) 7.5 × 104 ,b) 2.3× 10−3

CLASS – VIII TOPIC: Exponents and powers MM -30
Very short answers questions (5)
−2 −2
1. Find the value of 5
−1
2. Find the Cube of 2
3. Find the standard form of 0.00007.
4. Find usual form of 3.06 × 104
−3 57
5. Find multiplicative inverse of 5
MCQS (5)
1)93 ÷ 98 =
−5
a)95 b)9−5 𝑐)−95 𝑑)−9
2) The value of p ,for which 7 ÷ 7−𝑝 = 710 is
7

a)1 b)2 c)3 d) 4
3)𝑥 𝑚 𝑋𝑥 𝑛 is expressed as
a)𝑥 𝑚 +𝑛 b)𝑥 𝑚𝑛 c)𝑥 𝑚 −𝑛 d)𝑥 𝑚 ÷𝑛

4) 2−1 + 3−1 + 4−1 0 equals to
a)2+3+4 b)1+1+1 1 1 1 d)1
c)2 + 3 + 4
5) In 5𝑛 , n is known as
a) base b) exponent c)constant d)number

Short answer type questions (12)
8−1 𝑋 53
1) Evaluate : 4 −2
2) Find m so that (−7)𝑚 +1 𝑋( −7)5 = (−7)8
3) Simplify and express in exponential form : 25 ÷ 28 5 𝑋2−5
−1
1 −1 1 −1
4) Evaluate : −
3 4

55

5) Express following in usual form : a) 4.5 × 104 ,b) 5× 10−3
6) Express in standard form : a) 3080000 , b) 0.00067

Long answer type questions (8)
2 2𝑥+6 2 3 2 𝑥+2
9) Find x : 5 𝑋 5 = 5
10) In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness 0.016 mm.
Find the total thickness of stack in standard form.

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