Class 7Multiplication and Division

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(1) Simplif y f ollowing and write answer in exponential f orm

A)78 × 497 = 7

B)494 × 3438 × 495 = 7

C)84 × 46 × 46 × 28 ÷ 28 = 2

D)274 × 37 × 34 × 279 = 3

E)82 × 47 × 29 = 2

(2) Simplif y f ollowing and write answer in exponential f orm

A)96 × 93 × 279 × 278 = 3

B)23 × 23 ÷ 23 = 2

(3) Simplif y f ollowing and write answer in exponential f orm

A)259 × 252 × 1257 ÷ 57 = 5

B)3435 × 497 = 7

(4) Simplif y f ollowing and write answer in exponential f orm

A)1256 × 253 ÷ 53 = 5

B)95 × 277 ÷ 37 = 3

(5) Simplif y f ollowing and write answer in exponential f orm

A)1253 × 58 × 56 × 53 × 1259 ÷ 59 = 5

B)34 × 97 × 95 × 279 × 96 = 3

(6) Simplif y f ollowing and write answer in exponential f orm

A)48 × 89 = 2

B)498 × 3438 × 494 × 3432 × 494 ÷ 74 = 7

ID : in-7-Multiplication-and-Division [1]

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(7) Simplif y f ollowing and write answer in exponential f orm

A)86 × 23 × 45 = 2

B)1259 × 59 ÷ 59 = 5

(8) Simplif y f ollowing and write answer in exponential f orm

A)86 × 83 × 43 ÷ 23 = 2

B)1256 × 58 × 58 × 53 ÷ 53 = 5

(9) Simplif y f ollowing and write answer in exponential f orm

A)95 × 93 × 278 ÷ 38 = 3

B)255 × 259 ÷ 59 = 5

(10) Simplif y f ollowing and write answer in exponential f orm

A)1252 × 1255 × 58 × 1259 = 5

B)1252 × 57 = 5

(11) Simplif y f ollowing and write answer in exponential f orm

A)253 × 1257 × 258 × 1254 = 5

B)273 × 273 ÷ 33 = 3

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ID : in-7-Multiplication-and-Division [2]

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Answers

(1) A) 22

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 78 × 497 can be simplif ied as:

78 × 497

= (7)8 × (7 × 7)7

= (7)8 × (72)7

= 78 × 714

= 7 (8 + 14)

= 722

Step 3

Theref ore the value of 78 × 497 in exponential f orm is 722.

ID : in-7-Multiplication-and-Division [3]

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B) 42

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 494 × 3438 × 495 can be simplif ied as:

494 × 3438 × 495

= (7 × 7)4 × (7 × 7 × 7)8 × (7 × 7)5

= (72)4 × (73)8 × (72)5

= 78 × 724 × 710

= 7 (8 + 24 + 10)

= 742

Step 3

Theref ore the value of 494 × 3438 × 495 in exponential f orm is 742.

ID : in-7-Multiplication-and-Division [4]

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C) 36

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 84 × 46 × 46 × 28 ÷ 28 can be simplif ied as:

84 × 46 × 46 × 28 ÷ 28

= (2 × 2 × 2)4 × (2 × 2)6 × (2 × 2)6 × (2)8 ÷ 28

= (23)4 × (22)6 × (22)6 × (2)8 ÷ 28

= 212 × 212 × 212 × 28 ÷ 28

= 2(12 + 12 + 12 + 8 - 8 )

= 236

Step 3

Theref ore the value of 84 × 46 × 46 × 28 ÷ 28 in exponential f orm is 236 .

ID : in-7-Multiplication-and-Division [5]

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D) 50

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 274 × 37 × 34 × 279 can be simplif ied as:

274 × 37 × 34 × 279

= (3 × 3 × 3)4 × (3)7 × (3)4 × (3 × 3 × 3)9

= (33)4 × (3)7 × (3)4 × (33)9

= 312 × 37 × 34 × 327

= 3(12 + 7 + 4 + 27)

= 350

Step 3

Theref ore the value of 274 × 37 × 34 × 279 in exponential f orm is 350 .

ID : in-7-Multiplication-and-Division [6]

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E) 29

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 82 × 47 × 29 can be simplif ied as:

82 × 47 × 29

= (2 × 2 × 2)2 × (2 × 2)7 × (2)9

= (23)2 × (22)7 × (2)9

= 26 × 214 × 29

= 2(6 + 14 + 9)

= 229

Step 3

Theref ore the value of 82 × 47 × 29 in exponential f orm is 229 .

ID : in-7-Multiplication-and-Division [7]

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(2) A) 69

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 96 × 93 × 279 × 278 can be simplif ied as:

96 × 93 × 279 × 278

= (3 × 3)6 × (3 × 3)3 × (3 × 3 × 3)9 × (3 × 3 × 3)8

= (32)6 × (32)3 × (33)9 × (33)8

= 312 × 36 × 327 × 324

= 3(12 + 6 + 27 + 24)

= 369

Step 3

Theref ore the value of 96 × 93 × 279 × 278 in exponential f orm is 369 .

ID : in-7-Multiplication-and-Division [8]

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B) 3

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 23 × 23 ÷ 23 can be simplif ied as:

23 × 23 ÷ 23

= (2)3 × (2)3 ÷ 23

= (2)3 × (2)3 ÷ 23

= 23 × 23 ÷ 23

= 2(3 + 3 - 3)

= 23

Step 3

Theref ore the value of 23 × 23 ÷ 23 in exponential f orm is 23.

ID : in-7-Multiplication-and-Division [9]

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(3) A) 36

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 259 × 252 × 1257 ÷ 57 can be simplif ied as:

259 × 252 × 1257 ÷ 57

= (5 × 5)9 × (5 × 5)2 × (5 × 5 × 5)7 ÷ 57

= (52)9 × (52)2 × (53)7 ÷ 57

= 518 × 54 × 521 ÷ 57

= 5(18 + 4 + 21 - 7)

= 536

Step 3

Theref ore the value of 259 × 252 × 1257 ÷ 57 in exponential f orm is 536 .

ID : in-7-Multiplication-and-Division [10]

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B) 29

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 3435 × 497 can be simplif ied as:

3435 × 497

= (7 × 7 × 7)5 × (7 × 7)7

= (73)5 × (72)7

= 715 × 714

= 7 (15 + 14)

= 729

Step 3

Theref ore the value of 3435 × 497 in exponential f orm is 729 .

ID : in-7-Multiplication-and-Division [11]

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(4) A) 21

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 1256 × 253 ÷ 53 can be simplif ied as:

1256 × 253 ÷ 53

= (5 × 5 × 5)6 × (5 × 5)3 ÷ 53

= (53)6 × (52)3 ÷ 53

= 518 × 56 ÷ 53

= 5(18 + 6 - 3)

= 521

Step 3

Theref ore the value of 1256 × 253 ÷ 53 in exponential f orm is 521.

ID : in-7-Multiplication-and-Division [12]

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B) 24

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 95 × 277 ÷ 37 can be simplif ied as:

95 × 277 ÷ 37

= (3 × 3)5 × (3 × 3 × 3)7 ÷ 37

= (32)5 × (33)7 ÷ 37

= 310 × 321 ÷ 37

= 3(10 + 21 - 7)

= 324

Step 3

Theref ore the value of 95 × 277 ÷ 37 in exponential f orm is 324 .

ID : in-7-Multiplication-and-Division [13]

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(5) A) 44

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 1253 × 58 × 56 × 53 × 1259 ÷ 59 can be simplif ied as:

1253 × 58 × 56 × 53 × 1259 ÷ 59

= (5 × 5 × 5)3 × (5)8 × (5)6 × (5)3 × (5 × 5 × 5)9 ÷ 59

= (53)3 × (5)8 × (5)6 × (5)3 × (53)9 ÷ 59

= 59 × 58 × 56 × 53 × 527 ÷ 59

= 5(9 + 8 + 6 + 3 + 27 - 9)

= 544

Step 3

Theref ore the value of 1253 × 58 × 56 × 53 × 1259 ÷ 59 in exponential f orm is

544 .

ID : in-7-Multiplication-and-Division [14]

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B) 67

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 34 × 97 × 95 × 279 × 96 can be simplif ied as:

34 × 97 × 95 × 279 × 96

= (3)4 × (3 × 3)7 × (3 × 3)5 × (3 × 3 × 3)9 × (3 × 3)6

= (3)4 × (32)7 × (32)5 × (33)9 × (32)6

= 34 × 314 × 310 × 327 × 312

= 3(4 + 14 + 10 + 27 + 12)

= 367

Step 3

Theref ore the value of 34 × 97 × 95 × 279 × 96 in exponential f orm is 367 .

ID : in-7-Multiplication-and-Division [15]

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(6) A) 43

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 48 × 89 can be simplif ied as:

48 × 89

= (2 × 2)8 × (2 × 2 × 2)9

= (22)8 × (23)9

= 216 × 227

= 2(16 + 27)

= 243

Step 3

Theref ore the value of 48 × 89 in exponential f orm is 243.

ID : in-7-Multiplication-and-Division [16]

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B) 58

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 498 × 3438 × 494 × 3432 × 494 ÷ 74 can be simplif ied as:

498 × 3438 × 494 × 3432 × 494 ÷ 74

= (7 × 7)8 × (7 × 7 × 7)8 × (7 × 7)4 × (7 × 7 × 7)2 × (7 × 7)4 ÷ 74

= (72)8 × (73)8 × (72)4 × (73)2 × (72)4 ÷ 74

= 716 × 724 × 78 × 76 × 78 ÷ 74

= 7 (16 + 24 + 8 + 6 + 8 - 4)

= 758

Step 3

Theref ore the value of 498 × 3438 × 494 × 3432 × 494 ÷ 74 in exponential f orm

is 758.

ID : in-7-Multiplication-and-Division [17]

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(7) A) 31

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 86 × 23 × 45 can be simplif ied as:

86 × 23 × 45

= (2 × 2 × 2)6 × (2)3 × (2 × 2)5

= (23)6 × (2)3 × (22)5

= 218 × 23 × 210

= 2(18 + 3 + 10)

= 231

Step 3

Theref ore the value of 86 × 23 × 45 in exponential f orm is 231.

ID : in-7-Multiplication-and-Division [18]

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B) 27

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 1259 × 59 ÷ 59 can be simplif ied as:

1259 × 59 ÷ 59

= (5 × 5 × 5)9 × (5)9 ÷ 59

= (53)9 × (5)9 ÷ 59

= 527 × 59 ÷ 59

= 5(27 + 9 - 9 )

= 527

Step 3

Theref ore the value of 1259 × 59 ÷ 59 in exponential f orm is 527 .

ID : in-7-Multiplication-and-Division [19]

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(8) A) 30

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 86 × 83 × 43 ÷ 23 can be simplif ied as:

86 × 83 × 43 ÷ 23

= (2 × 2 × 2)6 × (2 × 2 × 2)3 × (2 × 2)3 ÷ 23

= (23)6 × (23)3 × (22)3 ÷ 23

= 218 × 29 × 26 ÷ 23

= 2(18 + 9 + 6 - 3)

= 230

Step 3

Theref ore the value of 86 × 83 × 43 ÷ 23 in exponential f orm is 230 .

ID : in-7-Multiplication-and-Division [20]

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B) 34

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 1256 × 58 × 58 × 53 ÷ 53 can be simplif ied as:

1256 × 58 × 58 × 53 ÷ 53

= (5 × 5 × 5)6 × (5)8 × (5)8 × (5)3 ÷ 53

= (53)6 × (5)8 × (5)8 × (5)3 ÷ 53

= 518 × 58 × 58 × 53 ÷ 53

= 5(18 + 8 + 8 + 3 - 3)

= 534

Step 3

Theref ore the value of 1256 × 58 × 58 × 53 ÷ 53 in exponential f orm is 534 .

ID : in-7-Multiplication-and-Division [21]

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(9) A) 32

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 95 × 93 × 278 ÷ 38 can be simplif ied as:

95 × 93 × 278 ÷ 38

= (3 × 3)5 × (3 × 3)3 × (3 × 3 × 3)8 ÷ 38

= (32)5 × (32)3 × (33)8 ÷ 38

= 310 × 36 × 324 ÷ 38

= 3(10 + 6 + 24 - 8)

= 332

Step 3

Theref ore the value of 95 × 93 × 278 ÷ 38 in exponential f orm is 332.

ID : in-7-Multiplication-and-Division [22]

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B) 19

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 255 × 259 ÷ 59 can be simplif ied as:

255 × 259 ÷ 59

= (5 × 5)5 × (5 × 5)9 ÷ 59

= (52)5 × (52)9 ÷ 59

= 510 × 518 ÷ 59

= 5(10 + 18 - 9)

= 519

Step 3

Theref ore the value of 255 × 259 ÷ 59 in exponential f orm is 519 .

ID : in-7-Multiplication-and-Division [23]

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(10) A) 56

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 1252 × 1255 × 58 × 1259 can be simplif ied as:

1252 × 1255 × 58 × 1259

= (5 × 5 × 5)2 × (5 × 5 × 5)5 × (5)8 × (5 × 5 × 5)9

= (53)2 × (53)5 × (5)8 × (53)9

= 56 × 515 × 58 × 527

= 5(6 + 15 + 8 + 27)

= 556

Step 3

Theref ore the value of 1252 × 1255 × 58 × 1259 in exponential f orm is 556 .

ID : in-7-Multiplication-and-Division [24]

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B) 13

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 1252 × 57 can be simplif ied as:

1252 × 57

= (5 × 5 × 5)2 × (5)7

= (53)2 × (5)7

= 56 × 57

= 5(6 + 7)

= 513

Step 3

Theref ore the value of 1252 × 57 in exponential f orm is 513.

ID : in-7-Multiplication-and-Division [25]

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(11) A) 55

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 253 × 1257 × 258 × 1254 can be simplif ied as:

253 × 1257 × 258 × 1254

= (5 × 5)3 × (5 × 5 × 5)7 × (5 × 5)8 × (5 × 5 × 5)4

= (52)3 × (53)7 × (52)8 × (53)4

= 56 × 521 × 516 × 512

= 5(6 + 21 + 16 + 12)

= 555

Step 3

Theref ore the value of 253 × 1257 × 258 × 1254 in exponential f orm is 555 .

ID : in-7-Multiplication-and-Division [26]

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B) 15

Step 1

Rules of the exponent:Rule 1: When you multiply two numbers with the same base, you add theexponents.Rule 2: When you divide two numbers with the same base, you subtract theexponents.Rule 3: When you have an exponent expression that is raised to a power, youcan multiply the exponent and power.

Step 2

First of all you have to simplif y each number with the same base.

Now 273 × 273 ÷ 33 can be simplif ied as:

273 × 273 ÷ 33

= (3 × 3 × 3)3 × (3 × 3 × 3)3 ÷ 33

= (33)3 × (33)3 ÷ 33

= 39 × 39 ÷ 33

= 3(9 + 9 - 3)

= 315

Step 3

Theref ore the value of 273 × 273 ÷ 33 in exponential f orm is 315 .

ID : in-7-Multiplication-and-Division [27]

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