ID : ww-7-Multiplication-and-Division [1]
Grade 7
Multiplication and Division
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Fill in t he blanks
(1)
Simplif y f ollowing and write answer in exponential f orm
A)
B)
C)
D)
E)
(2)
49 × 45 = 2
7 3 × 493 ÷ 7 3 = 7
56 × 1254 × 55 × 58 × 1253 = 5
84 × 88 = 2
Simplif y f ollowing and write answer in exponential f orm
A)
B)
(3)
38 × 39 ÷ 39 = 3
3439 × 7 4 = 7
7 8 × 7 6 × 3439 × 3433 = 7
Simplif y f ollowing and write answer in exponential f orm
A)
B)
96 × 27 7 × 92 × 96 = 3
82 × 25 × 28 ÷ 28 = 2
(4) Simplif y f ollowing and write answer in exponential f orm
A)
B)
(5)
58 × 1254 × 259 = 5
1259 × 59 = 5
Simplif y f ollowing and write answer in exponential f orm
A)
B)
57 × 1258 × 52 × 1259 = 5
259 × 56 × 254 ÷ 54 = 5
(6) Simplif y f ollowing and write answer in exponential f orm
A)
B)
3438 × 3435 × 499 × 494 = 7
88 × 84 ÷ 24 = 2
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ID : ww-7-Multiplication-and-Division [2]
(7) Simplif y f ollowing and write answer in exponential f orm
A)
B)
(8)
252 × 1257 × 58 = 5
27 3 × 94 × 35 = 3
Simplif y f ollowing and write answer in exponential f orm
A)
B)
7 9 × 3437 × 3432 × 3435 ÷ 7 5 = 7
495 × 7 4 × 497 × 497 ÷ 7 7 = 7
(9) Simplif y f ollowing and write answer in exponential f orm
A)
B)
496 × 3436 = 7
27 6 × 92 × 99 = 3
(10) Simplif y f ollowing and write answer in exponential f orm
A)
B)
53 × 258 = 5
39 × 38 × 34 × 27 7 × 33 = 3
(11) Simplif y f ollowing and write answer in exponential f orm
A)
B)
27 5 × 94 × 94 × 27 9 ÷ 39 = 3
27 × 82 × 82 × 89 = 2
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ID : ww-7-Multiplication-and-Division [3]
Answers
(1)
A)
8
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 38 × 39 ÷ 39 can be simplif ied as:
38 × 39 ÷ 39
= (3)8 × (3)9 ÷ 39
= (3)8 × (3)9 ÷ 39
= 38 × 39 ÷ 39
= 3(8 + 9 - 9 )
= 38
Step 3
T heref ore the value of 38 × 39 ÷ 39 in exponential f orm is 38.
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ID : ww-7-Multiplication-and-Division [4]
B)
28
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 4 9 × 4 5 can be simplif ied as:
49 × 45
= (2 × 2)9 × (2 × 2)5
= (22)9 × (22)5
= 218 × 210
= 2(18 + 10 )
= 228
Step 3
T heref ore the value of 4 9 × 4 5 in exponential f orm is 228.
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ID : ww-7-Multiplication-and-Division [5]
C)
6
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 7 3 × 493 ÷ 7 3 can be simplif ied as:
7 3 × 493 ÷ 7 3
= (7)3 × (7 × 7)3 ÷ 7 3
= (7)3 × (7 2)3 ÷ 7 3
= 73 × 76 ÷ 73
= 7 (3 + 6 - 3)
= 76
Step 3
T heref ore the value of 7 3 × 493 ÷ 7 3 in exponential f orm is 7 6 .
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ID : ww-7-Multiplication-and-Division [6]
D)
40
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 56 × 1254 × 55 × 58 × 1253 can be simplif ied as:
56 × 1254 × 55 × 58 × 1253
= (5)6 × (5 × 5 × 5)4 × (5)5 × (5)8 × (5 × 5 × 5)3
= (5)6 × (53)4 × (5)5 × (5)8 × (53)3
= 56 × 512 × 55 × 58 × 59
= 5(6 + 12 + 5 + 8 + 9 )
= 540
Step 3
T heref ore the value of 56 × 1254 × 55 × 58 × 1253 in exponential f orm is 54 0 .
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ID : ww-7-Multiplication-and-Division [7]
E)
36
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 84 × 88 can be simplif ied as:
84 × 88
= (2 × 2 × 2)4 × (2 × 2 × 2)8
= (23)4 × (23)8
= 212 × 224
= 2(12 + 24)
= 236
Step 3
T heref ore the value of 84 × 88 in exponential f orm is 236 .
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ID : ww-7-Multiplication-and-Division [8]
(2)
A)
31
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 3439 × 7 4 can be simplif ied as:
3439 × 7 4
= (7 × 7 × 7)9 × (7)4
= (7 3)9 × (7)4
= 7 27 × 7 4
= 7 (27 + 4)
= 7 31
Step 3
T heref ore the value of 3439 × 7 4 in exponential f orm is 7 31.
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ID : ww-7-Multiplication-and-Division [9]
B)
50
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 7 8 × 7 6 × 3439 × 3433 can be simplif ied as:
7 8 × 7 6 × 3439 × 3433
= (7)8 × (7)6 × (7 × 7 × 7)9 × (7 × 7 × 7)3
= (7)8 × (7)6 × (7 3)9 × (7 3)3
= 7 8 × 7 6 × 7 27 × 7 9
= 7 (8 + 6 + 27 + 9 )
= 7 50
Step 3
T heref ore the value of 7 8 × 7 6 × 3439 × 3433 in exponential f orm is 7 5 0 .
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ID : ww-7-Multiplication-and-Division [10]
(3)
A)
49
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 96 × 27 7 × 92 × 96 can be simplif ied as:
96 × 27 7 × 92 × 96
= (3 × 3)6 × (3 × 3 × 3)7 × (3 × 3)2 × (3 × 3)6
= (32)6 × (33)7 × (32)2 × (32)6
= 312 × 321 × 34 × 312
= 3(12 + 21 + 4 + 12)
= 349
Step 3
T heref ore the value of 96 × 27 7 × 92 × 96 in exponential f orm is 34 9 .
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ID : ww-7-Multiplication-and-Division [11]
B)
11
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 82 × 25 × 28 ÷ 28 can be simplif ied as:
82 × 25 × 28 ÷ 28
= (2 × 2 × 2)2 × (2)5 × (2)8 ÷ 28
= (23)2 × (2)5 × (2)8 ÷ 28
= 26 × 25 × 28 ÷ 28
= 2(6 + 5 + 8 - 8 )
= 211
Step 3
T heref ore the value of 82 × 25 × 28 ÷ 28 in exponential f orm is 211.
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ID : ww-7-Multiplication-and-Division [12]
(4)
A)
38
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 58 × 1254 × 259 can be simplif ied as:
58 × 1254 × 259
= (5)8 × (5 × 5 × 5)4 × (5 × 5)9
= (5)8 × (53)4 × (52)9
= 58 × 512 × 518
= 5(8 + 12 + 18 )
= 538
Step 3
T heref ore the value of 58 × 1254 × 259 in exponential f orm is 538.
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ID : ww-7-Multiplication-and-Division [13]
B)
36
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 1259 × 59 can be simplif ied as:
1259 × 59
= (5 × 5 × 5)9 × (5)9
= (53)9 × (5)9
= 527 × 59
= 5(27 + 9 )
= 536
Step 3
T heref ore the value of 1259 × 59 in exponential f orm is 536 .
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ID : ww-7-Multiplication-and-Division [14]
(5)
A)
60
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 57 × 1258 × 52 × 1259 can be simplif ied as:
57 × 1258 × 52 × 1259
= (5)7 × (5 × 5 × 5)8 × (5)2 × (5 × 5 × 5)9
= (5)7 × (53)8 × (5)2 × (53)9
= 57 × 524 × 52 × 527
= 5(7 + 24 + 2 + 27)
= 56 0
Step 3
T heref ore the value of 57 × 1258 × 52 × 1259 in exponential f orm is 56 0 .
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ID : ww-7-Multiplication-and-Division [15]
B)
28
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 259 × 56 × 254 ÷ 54 can be simplif ied as:
259 × 56 × 254 ÷ 54
= (5 × 5)9 × (5)6 × (5 × 5)4 ÷ 54
= (52)9 × (5)6 × (52)4 ÷ 54
= 518 × 56 × 58 ÷ 54
= 5(18 + 6 + 8 - 4)
= 528
Step 3
T heref ore the value of 259 × 56 × 254 ÷ 54 in exponential f orm is 528.
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ID : ww-7-Multiplication-and-Division [16]
(6)
A)
65
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 3438 × 3435 × 499 × 494 can be simplif ied as:
3438 × 3435 × 499 × 494
= (7 × 7 × 7)8 × (7 × 7 × 7)5 × (7 × 7)9 × (7 × 7)4
= (7 3)8 × (7 3)5 × (7 2)9 × (7 2)4
= 7 24 × 7 15 × 7 18 × 7 8
= 7 (24 + 15 + 18 + 8 )
= 765
Step 3
T heref ore the value of 3438 × 3435 × 499 × 494 in exponential f orm is 7 6 5 .
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ID : ww-7-Multiplication-and-Division [17]
B)
32
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 88 × 84 ÷ 24 can be simplif ied as:
88 × 84 ÷ 24
= (2 × 2 × 2)8 × (2 × 2 × 2)4 ÷ 24
= (23)8 × (23)4 ÷ 24
= 224 × 212 ÷ 24
= 2(24 + 12 - 4)
= 232
Step 3
T heref ore the value of 88 × 84 ÷ 24 in exponential f orm is 232.
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ID : ww-7-Multiplication-and-Division [18]
(7)
A)
33
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 252 × 1257 × 58 can be simplif ied as:
252 × 1257 × 58
= (5 × 5)2 × (5 × 5 × 5)7 × (5)8
= (52)2 × (53)7 × (5)8
= 54 × 521 × 58
= 5(4 + 21 + 8 )
= 533
Step 3
T heref ore the value of 252 × 1257 × 58 in exponential f orm is 533.
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ID : ww-7-Multiplication-and-Division [19]
B)
22
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 27 3 × 94 × 35 can be simplif ied as:
27 3 × 94 × 35
= (3 × 3 × 3)3 × (3 × 3)4 × (3)5
= (33)3 × (32)4 × (3)5
= 39 × 38 × 35
= 3(9 + 8 + 5)
= 322
Step 3
T heref ore the value of 27 3 × 94 × 35 in exponential f orm is 322.
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ID : ww-7-Multiplication-and-Division [20]
(8)
A)
46
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 7 9 × 3437 × 3432 × 3435 ÷ 7 5 can be simplif ied as:
7 9 × 3437 × 3432 × 3435 ÷ 7 5
= (7)9 × (7 × 7 × 7)7 × (7 × 7 × 7)2 × (7 × 7 × 7)5 ÷ 7 5
= (7)9 × (7 3)7 × (7 3)2 × (7 3)5 ÷ 7 5
= 7 9 × 7 21 × 7 6 × 7 15 ÷ 7 5
= 7 (9 + 21 + 6 + 15 - 5)
= 7 46
Step 3
T heref ore the value of 7 9 × 3437 × 3432 × 3435 ÷ 7 5 in exponential f orm is 7 4 6 .
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ID : ww-7-Multiplication-and-Division [21]
B)
35
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 495 × 7 4 × 497 × 497 ÷ 7 7 can be simplif ied as:
495 × 7 4 × 497 × 497 ÷ 7 7
= (7 × 7)5 × (7)4 × (7 × 7)7 × (7 × 7)7 ÷ 7 7
= (7 2)5 × (7)4 × (7 2)7 × (7 2)7 ÷ 7 7
= 7 10 × 7 4 × 7 14 × 7 14 ÷ 7 7
= 7 (10 + 4 + 14 + 14 - 7)
= 7 35
Step 3
T heref ore the value of 495 × 7 4 × 497 × 497 ÷ 7 7 in exponential f orm is 7 35 .
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ID : ww-7-Multiplication-and-Division [22]
(9)
A)
30
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 496 × 3436 can be simplif ied as:
496 × 3436
= (7 × 7)6 × (7 × 7 × 7)6
= (7 2)6 × (7 3)6
= 7 12 × 7 18
= 7 (12 + 18 )
= 7 30
Step 3
T heref ore the value of 496 × 3436 in exponential f orm is 7 30 .
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ID : ww-7-Multiplication-and-Division [23]
B)
40
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 27 6 × 92 × 99 can be simplif ied as:
27 6 × 92 × 99
= (3 × 3 × 3)6 × (3 × 3)2 × (3 × 3)9
= (33)6 × (32)2 × (32)9
= 318 × 34 × 318
= 3(18 + 4 + 18 )
= 340
Step 3
T heref ore the value of 27 6 × 92 × 99 in exponential f orm is 34 0 .
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ID : ww-7-Multiplication-and-Division [24]
(10) A)
19
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 53 × 258 can be simplif ied as:
53 × 258
= (5)3 × (5 × 5)8
= (5)3 × (52)8
= 53 × 516
= 5(3 + 16 )
= 519
Step 3
T heref ore the value of 53 × 258 in exponential f orm is 519 .
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ID : ww-7-Multiplication-and-Division [25]
B)
45
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 39 × 38 × 34 × 27 7 × 33 can be simplif ied as:
39 × 38 × 34 × 27 7 × 33
= (3)9 × (3)8 × (3)4 × (3 × 3 × 3)7 × (3)3
= (3)9 × (3)8 × (3)4 × (33)7 × (3)3
= 39 × 38 × 34 × 321 × 33
= 3(9 + 8 + 4 + 21 + 3)
= 345
Step 3
T heref ore the value of 39 × 38 × 34 × 27 7 × 33 in exponential f orm is 34 5 .
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ID : ww-7-Multiplication-and-Division [26]
(11) A)
49
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 27 5 × 94 × 94 × 27 9 ÷ 39 can be simplif ied as:
27 5 × 94 × 94 × 27 9 ÷ 39
= (3 × 3 × 3)5 × (3 × 3)4 × (3 × 3)4 × (3 × 3 × 3)9 ÷ 39
= (33)5 × (32)4 × (32)4 × (33)9 ÷ 39
= 315 × 38 × 38 × 327 ÷ 39
= 3(15 + 8 + 8 + 27 - 9 )
= 349
Step 3
T heref ore the value of 27 5 × 94 × 94 × 27 9 ÷ 39 in exponential f orm is 34 9 .
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ID : ww-7-Multiplication-and-Division [27]
B)
46
Step 1
Rules of the exponent:
Rule 1: When you multiply two numbers with the same base, you add the
exponents.
Rule 2: When you divide two numbers with the same base, you subtract the
exponents.
Rule 3: When you have an exponent expression that is raised to a power, you
can multiply the exponent and power.
Step 2
First of all you have to simplif y each number with the same base.
Now 27 × 82 × 82 × 89 can be simplif ied as:
27 × 82 × 82 × 89
= (2)7 × (2 × 2 × 2)2 × (2 × 2 × 2)2 × (2 × 2 × 2)9
= (2)7 × (23)2 × (23)2 × (23)9
= 27 × 26 × 26 × 227
= 2(7 + 6 + 6 + 27)
= 246
Step 3
T heref ore the value of 27 × 82 × 82 × 89 in exponential f orm is 24 6 .
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