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Page No 39:

Question O1:

What is the base and exponent in 73?

Answer:

In, the base is 7 and the exponent is 3.

Page No 39:

Question W1:

Write these as you read them.

(1) 23

(2) 35

(3) 67

(4) 1010

(5) (−2)5

(6)

(7) (32)2

(8) 4×32

(9) (73)5

(10) (−3)7

Answer:

(1) 23 can be read as “two cube.”

(2) 35 can be read as “three to the power of five.”

(3) 67 can be read as “six to the power of seven.”

(4) 1010 can be read as “ten to the power of ten.”

(5) (−2)5 can be read as “minus two to the power of five.”

(6)can be read as “minus two thirds to the power of four.”

(7) (32)2 can be read as “three square whole to the power of two.”

(8) 4×32 can be read as “four into three square.”

(9) (73)5 can be read as “seven cube whole to the power of five.”

(10) (−3)7 can be read as “minus three to the power of seven.”

Page No 39:

Question O2:

What is the value of 23?


 

Answer:

The value of is.

Page No 39:

Question W2:

Write these exponential form.

(1) five to the power of four

(2) three to the power of two (three square)

(3) minus ten to the power of five

(4) one third to the power of three

(5) two cubed to the power of four

Answer:

(1) Five to the power of four = 54

(2) Three to the power of two (three square) = 32

(3) Minus ten to the power of five = (−10)5

(4) One third to the power of three =

(5) Two cubed to the power of four = (23)4

Page No 39:

Question O3:

What is the value of 80?


 

Answer:

The value of is 1. [Value of any non zero number with zero exponent is always 1.]



Page No 40:

Question W3:

Mention the base and the exponent

(1) 103

(2) 24

(3) 45

(4) 50

(5) 72

(6) (−6)3

(7)

(8) (0.5)3

(9)

(10) (32)2

Answer:

(1) 103

Base = 10, Exponent = 3

(2) 24

Base = 2, Exponent = 4

(3) 45

Base = 4, Exponent = 5

(4) 50

Base = 5, Exponent = 0

(5) 72

Base = 7, Exponent = 2

(6) (−6)3

Base = − 6, Exponent = 3

(7)

Base =, Exponent = 4

(8) (0.5)3

Base = 0.5, Exponent = 3

(9)

Base = , Exponent = 5

(10) (32)2

Base = 32, Exponent = 2

Page No 40:

Question W4:

Expand the following exponential numbers:

(1) 23

(2) 32

(3) (−4)4

(4)

(5) (52)3

Answer:

(1) 23 = 2 × 2 × 2

(2) 32 = 3 × 3

(3) (−4)4 = (−4) × (−4) × (−4) × (−4)

(4) = ××

(5) (52)3 = 52×52×52

Page No 40:

Question W5:

Write these in exponential form.

(1) 6 × 6 × 6 × 6

(2) (−5) × (−5) × (−5)

(3)

(4) 0.2 × 0.2 × 0.2

(5) (32) × (32) × (32)

Answer:

(1) 6 × 6 × 6 × 6 = 64

(2) (−5) × (−5) × (−5) = (−5)3

(3)

(4) 0.2 × 0.2 × 0.2 = (0.2)3

(5) (32) × (32) × (32) = (32)3



Page No 41:

Question W6:

Fill in the blanks with suitable answers:

(1) The repeated form of multiplication of the same number is …….. .

(2) Exponential numbers include …….. and exponents.

(3) The number of times the base is multiplied is indicated by …….. .

(4)

(5)

Answer:

(1) The repeated form of multiplication of the same number is exponent.

(2) Exponential numbers include base numbers and exponents.

(3) The number of times the base is multiplied is indicated by power index.

(4) 27 = 3 × 3 × 3 = 33

(5)



Page No 42:

Question O1:

Mention the squares of (a) +7 (b) (−4)

Answer:

(a) 49

(b) 16

Page No 42:

Question W1:

Write the squares of:

(1) 3

(2) −5

(3) +4

(4) −2

(5) +6

(6)

(7)

(8)

Answer:

(1) 32 = 3 × 3 = 9

Thus, the square of 3 is 9.

(2) (−5)2 = (−5) × (−5) = + 25

Thus, the square of −5 is +25.

(3) (+4)2 = 4 × 4 = 16

Thus, the square of +4 is 16.

(4) (−2)2 = (−2) × (−2) = +4

Thus, the square of −2 is +4.

(5) (+6)2 = 6×6 = 36

Thus, the square of +6 is 36.

(6) = × =

Thus, the square of is.

(7)

Thus, the square of is.

(8)

Thus, the square of is.

Page No 42:

Question O2:

Give the cubes of (a) +5 (b) (−6)

Answer:

(a) 125

(b) −216

Page No 42:

Question W2:

Write the cubes of:

(1) −2

(2) +1

(3) −5

(4) +7

(5) −10

(6) 2

(7) 3

(8) 10

(9)

(10)

Answer:

(1) (−2)3 = (−2) × (−2) × (−2) = − 8

Thus, the cube of −2 is −8.

(2) (+1)3 = (+1) × (+1) × (+1) = 1

Thus, the cube of +1 is 1.

(3) (−5)3 = (−5) × (−5) × (−5) = −125

Thus, the cube of −5 is −125.

(4) (+7)3 = (+7) × (+7) × (+7) = 343

Thus, the cube of +7 is 343.

(5) (−10)3 = (−10) × (−10) × (−10) = −1000

Thus, the cube of −10 is −1000.

(6) 23 = 2 × 2 ×2 = 8

Thus, the cube of 2 is 8.

(7) 33 = 3 × 3 × 3 = 27

Thus, the cube of 3 is 27.

(8) 103 = 10 × 10 ×10 = 1000

Thus, the cube of 10 is 1000.

(9)

Thus, the cube of is.

(10)

Thus, the cube of is .



Page No 43:

Question W3:

Write the exponents for the base given.

(1) 125 with 5 as base

(2) −343 with (−7) as base

(3) 32 with 2 as base

(4) 10,000 with (−10) as base

(5) −243 with (−3) as base

Answer:

(1) 125 = 5 × 5 × 5 = 53

Thus, the exponent is 53

(2) −343 = (−7) × (−7) × (−7) = (−7)3

Thus, the exponent is (−7)3

(3) 32 = 2 × 2 × 2 × 2 × 2 = 25

Thus, the exponent is 25.

(4) 10000 = (−10) × (−10) × (−10) × (−10) = 104

Thus, the exponent is (−10)4.

(5) −243 = (−3) × (−3) × (−3) × (−3) × (−3) = (−3)5

Thus, the exponent is (−3)5.

Page No 43:

Question W4:

Express the exponential form with prime number as base.

(1) 4

(2) 8

(3) 16

(4) 49

(5) 81

Answer:

(1) 4 = 2 × 2 = 22

(2) 8 = 2 × 2 × 2 = 23

(3) 16 = 2 × 2 × 2 × 2 = 24

(4) 49 = 7 × 7 = 72

(5) 81 = 3 × 3 × 3 × 3 = 34

Page No 43:

Question W5:

Write the given fractions in exponential form:

(1)

(2)

(3)

(4)

(5)

Answer:

(1)

(2)

(3)

(4)

(5)



Page No 46:

Question O1:

Mention the values of

(a) 32

(b) 52

(c) (−4)2

(d)

Answer:

(a) 9

(b) 25

(c) 16

(d) .

Page No 46:

Question W1:

Find the squares of:

(1) 32

(2) 52

(3) (−4)2

(4) (−2)2

(5) (−52)2

Answer:

(1) 32 = 3 × 3 = 9

(2) 52 = 5 × 5 = 25

(3) (−4)2 = (−4) × (−4) = +16

(4) (−2)2 = (−2) × (−2) = +4

(5) (−52)2 = (−52)× (−52) = (−25)× (−25) = +625

Page No 46:

Question W2:

Find the cubes of:

(1) (1)3

(2) (−2)3

(3) (3)3

(4) (4)3

(5) (−5)3

(6) (23)3

Answer:

(1) (1)3 = 1 × 1 × 1 = 1

(2) (−2)3 = (−2) × (−2) × (−2) = −8

(3) (3)3 = 3 × 3 × 3 = 27

(4) (4)3 = 4 × 4 × 4 = 64

(5) (−5)3 = (−5) × (−5) ×(−5) = −125

(6) (23)3 = 23 × 23 × 23 = 8 × 8 × 8 = 512

Page No 46:

Question W3:

Find the values of exponential numbers.

(1) 44

(2) 25

(3) 64

(4) (−3)4

(5) (−5)3

Answer:

(1) 44 = 4 × 4 × 4 × 4 = 256

44 = 256

(2) 25 = 2 × 2 × 2 × 2 × 2 = 32

25 = 32

(3) 64 = 6 × 6 × 6 × 6 = 1296

64 = 1296

(4) (−3)4 = (−3) × (−3) × (−3) × (−3) = +81

(−3)4 = +81

(5) (−5)3 = (−5) × (−5) × (−5) = −125

(−5)3 = −125

Page No 46:

Question W4:

Find the values of exponential numbers.

(1) (12)2

(2) (22)2

(3) (12)3

(4) (32)3

(5) (20)2

Answer:

(1) (12)2 = 12 × 12 = 1 × 1 = 1

(12)2 = 1

(2) (22)2 = 22 × 22 = 4 × 4 = 16

(22)2 = 16

(3) (12)3 = 12×12 = 1 × 1 = 1

(12)3 = 1

(4) (32)3 = 32 × 32 × 32 = 9 × 9 × 9 = 729

(32)3 = 729

(5) (20)2 = 20 ×2 0 = 1×1 = 1

(20)2 = 1



Page No 47:

Question W5:

Find the values of the following fractions which are in the exponential form:

(1)

(2)

(3)

(4)

(5)

Answer:

(1)

Thus,

(2)

Thus,

(3)

Thus,

(4)

Thus,

(5)

Thus,



Page No 48:

Question W1:

Fill in the blanks with proper answers:

(1) When a negative number is raised to an even power, the sign of the number is ……. .

(2) When a positive number is raised to an odd power, the sign of the number is …….. .

(3) When a negative number is raised to an odd power, then the sign of the number is ……. .

(4) (−4)2 = ……

(5) (−3)3 = ……

Answer:

(1) When a negative number is raised to an even power, the sign of the number is positive .

(2) When a positive number is raised to an odd power, the sign of the number is positive .

(3) When a negative number is raised to an odd power, then the sign of the number is negative .

(4) (−4)2 = +16

Explanation: (−4)2 = (−4)× (−4) = +16

(5) (−3)3 = −27

Explanation: (−3)3 = (−3)× (−3) × (−3) = −27



Page No 49:

Question W2:

Say whether the following are true or false:

 

True

False

(1) (−3)3 = +27

   

(2) (+2)4 = −16

   

(3) (−5)2 = +25

   

(4) (+7)3 = −147

   

(5)

   

Answer:

The complete table is:

 

True

False

(1) (−3)3 = +27

 

False

(2) (+2)4 = −16

 

False

(3) (−5)2 = +25

True

 

(4) (+7)3 = −147

 

False

(5)

True

 

Explanation:

(−3)3= (−3) × (−3) × (−3) = −27

(+2)4 = 2 × 2 × 2 × 2 = +16

(−5)2 = 5 × 5 = +25

(+7)3 = 7 × 7 × 7= +343

Page No 49:

Question W3:

(1) 22 + 32

(2) 32 − 22

(3) 22 × 33

(4) (−2)2 × (1)2

(5) 12 + 52

(6) 12 + 20

(7) 70 + 12

(8) 61 − 40

(9) 100 − 20

(10) 51 × 31

Answer:

(1) 22 + 32 = 2 × 2 + 3 × 3= 4 + 9 = 13

(2) 32 − 22 = 3 × 3 − 2 × 2 = 9 − 4 = 5

(3) 22 × 33 = 2 × 2 × 3 × 3 × 3 = 4 × 27 = 108

(4) (−2)2 × (1)2 = (−2) ×(−2) × 1 × 1 = 4 × 1 = 4

(5) 12 + 52 = 1 × 1 + 5 × 5 = 1 + 25 = 26

(6) 12 + 20 = 1 × 1 + 1 = 1 + 1 = 2

(7) 70 + 12 =1 + 1 × 1 = 1 + 1 = 2

(8) 61 − 40 = 6 − 1 = 5

(9) 100 − 20 =1 − 1 = 0

(10) 51 × 31 = 5 × 3 = 15

Page No 49:

Question W4:

(1) 42 + 24 − 32

(2) 33 − 22 + 20

(3) 53 − 22 + 40

(4) 61 + 50 − 41

(5) (−2)2 + 12 − 22

Answer:

(1) 42 + 24 − 32 =4 × 4 + 2 × 2 × 2 × 2 − 3 × 3 = 16 + 16 − 9 = 23

(2) 33 − 22 + 20 = 3 × 3 × 3 − 2 × 2 + 1 = 27 − 4 +1= 24

(3) 53 − 22 + 40 = 5 × 5 × 5 − 2 × 2 + 1 = 125 − 4 +1= 122

(4) 61 + 50 − 41 = 6 + 1 − 4 = 3

(5) (−2)2 + 12 − 22 = (−2) × (−2) + 1 × 1 − 2 × 2 = 4 + 1 − 4 = 1



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