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#### Question O1:

What is the base and exponent in 73?

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

#### 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

(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.”

#### Question O2:

What is the value of 23?

The value of is.

#### 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

(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

#### Question O3:

What is the value of 80?

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

#### 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

(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

#### Question W4:

Expand the following exponential numbers:

(1) 23

(2) 32

(3) (−4)4

(4)

(5) (52)3

(1) 23 = 2 × 2 × 2

(2) 32 = 3 × 3

(3) (−4)4 = (−4) × (−4) × (−4) × (−4)

(4) = ××

(5) (52)3 = 52×52×52

#### 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)

(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

#### 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)

(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)

#### Question O1:

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

(a) 49

(b) 16

#### Question W1:

Write the squares of:

(1) 3

(2) −5

(3) +4

(4) −2

(5) +6

(6)

(7)

(8)

(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.

#### Question O2:

Give the cubes of (a) +5 (b) (−6)

(a) 125

(b) −216

#### Question W2:

Write the cubes of:

(1) −2

(2) +1

(3) −5

(4) +7

(5) −10

(6) 2

(7) 3

(8) 10

(9)

(10)

(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 .

#### 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

(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.

#### Question W4:

Express the exponential form with prime number as base.

(1) 4

(2) 8

(3) 16

(4) 49

(5) 81

(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

#### Question W5:

Write the given fractions in exponential form:

(1)

(2)

(3)

(4)

(5)

(1)

(2)

(3)

(4)

(5)

#### Question O1:

Mention the values of

(a) 32

(b) 52

(c) (−4)2

(d)

(a) 9

(b) 25

(c) 16

(d) .

#### Question W1:

Find the squares of:

(1) 32

(2) 52

(3) (−4)2

(4) (−2)2

(5) (−52)2

(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

#### Question W2:

Find the cubes of:

(1) (1)3

(2) (−2)3

(3) (3)3

(4) (4)3

(5) (−5)3

(6) (23)3

(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

#### Question W3:

Find the values of exponential numbers.

(1) 44

(2) 25

(3) 64

(4) (−3)4

(5) (−5)3

(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

#### Question W4:

Find the values of exponential numbers.

(1) (12)2

(2) (22)2

(3) (12)3

(4) (32)3

(5) (20)2

(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

#### Question W5:

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

(1)

(2)

(3)

(4)

(5)

(1)

Thus,

(2)

Thus,

(3)

Thus,

(4)

Thus,

(5)

Thus,

#### 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 = ……

(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

#### 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)

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

#### 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

(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

#### Question W4:

(1) 42 + 24 − 32

(2) 33 − 22 + 20

(3) 53 − 22 + 40

(4) 61 + 50 − 41

(5) (−2)2 + 12 − 22

(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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