Grade 7 Exponents and Powers For more such worksheets visit www.edugain.com Answer the questions (1) Solve the following and write in the simplest fraction form. (2) (3) (4) Find the value of the following: A) 8 2 B) (-9) 2 C) 6 2 D) (-10) 3 (5) If 2 p + 2 p + 1 = 12, find the value of p. (6) Write the number for the following expanded forms: A) 5×10 1 + 0×10 6 + 4×10 2 + 5×10 2 + 0×10 1 + 3×10 8 + 9×10 0 B) 0×10 5 + 0×10 0 + 6×10 1 + 6×10 8 + 0×10 4 (7) Simplify the following and write the answer in the exponential form A) 7 8 × 7 4 7 3 × 7 6 × 7 7 × 7 8 × 7 9 × 7 9 B) 11 8 × 11 5 11 9 × 11 4 × 11 6 × 11 7 C) 5 4 × 5 9 5 9 × 5 9 × 5 2 × 5 5 D) 17 3 × 17 3 × 17 8 17 5 × 17 7 × 17 7 × 17 2 × 17 7 × 17 2 (8) If x = 1 and y = 5, find the value of . (9) = ? (10) Find the value of x. (11) Solve the following and write in the simplest form of fraction. ID : ae-7-Exponents-and-Powers [1] Copyright 2017 www.edugain.com Personal use only. Commercial use is strictly prohibited.
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Grade 7 Exponents and PowersRule 1: When we multiply two numbers with the same base, we add the exponents. Rule 2: When we divide two numbers with the same base, we subtract the exponents.
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Grade 7Exponents and Powers
For more such worksheets visit www.edugain.com
Answer the questions
(1) Solve the following and write in the simplest fraction form.
(2)
(3)
(4) Find the value of the following:
A) 82 B) (-9)2
C) 62 D) (-10)3
(5) If 2p + 2p + 1 = 12, find the value of p.
(6) Write the number for the following expanded forms:
(12) Ferran plants a dandelion on his 8 th birthday. If the plant has one dandelion to start with and thenumber of dandelions doubles every week then how many dandelions will be there after x weeks?
(13) Simplify the following and write the answer in the exponential form.
Hence, the number for the expended form 5×101 + 0×106 + 4×102 + 5×102 + 0×101 +
3×108 + 9×100 is 300000959.
B) 600000060
Step 1
0×105 + 0×100 + 6×101 + 6×108 + 0×104 can be solved by the following steps:
0×105 + 0×100 + 6×101 + 6×108 + 0×104
= 0 + 0 + 60 + 600000000 + 0= 600000060
Step 2
Hence, the number for the expended form 0×105 + 0×100 + 6×101 + 6×108 + 0×104 is600000060.
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(7) A) 736
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
78 × 74
73 × 76 × 77 × 78 × 79 × 79 can be simplified as:
78 × 74
73 × 76 × 77 × 78 × 79 × 79
= 7(8 + 4)
7(3 + 6) × 7(7 + 8 + 9 + 9)
= 712
79 × 733
= 712 ÷ 79 × 733
= 7(12 - 9 + 33)
= 736
Step 3
Hence, the exponential form of 78 × 74
73 × 76 × 77 × 78 × 79 × 79 is 736.
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B) 1121
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
118 × 115
119 × 114 × 116 × 117 can be simplified as:
118 × 115
119 × 114 × 116 × 117
= 11(8 + 5)
11(9) × 11(4 + 6 + 7)
= 1113
119 × 1117
= 1113 ÷ 119 × 1117
= 11(13 - 9 + 17)
= 1121
Step 3
Hence, the exponential form of 118 × 115
119 × 114 × 116 × 117 is 1121.
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C) 52
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
54 × 59
59 × 59 × 52 × 55 can be simplified as:
54 × 59
59 × 59 × 52 × 55
= 5(4 - 9)
5(9 + 9) × 5(2 + 5)
= 54
518 × 57
= 54 ÷ 518 × 57
= 5(4 - 18 + 7)
= 52
Step 3
Hence, the exponential form of 54 × 59
59 × 59 × 52 × 55 is 52.
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D) 172
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
173 × 173 × 178
175 × 177 × 177 × 172 × 177 × 172 can be simplified as:
173 × 173 × 178
175 × 177 × 177 × 172 × 177 × 172
= 17(3 + 3 - 8)
17(5 + 7 + 7 + 2) × 17(7 + 2)
= 176
1721 × 179
= 176 ÷ 1721 × 179
= 17(6 - 21 + 9)
= 172
Step 3
Hence, the exponential form of 173 × 173 × 178
175 × 177 × 177 × 172 × 177 × 172 is 172.
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(8) 1
5
Step 1
According to the question, we have to find out the value of ( x
y )x, where x = 1 and y = 5.
Step 2
Let us put the values of x and y in ( x
y )x
( x
y )x = (
1
5 )1
= 1
5 .
Step 3
Hence, the value of ( x
y )x, where x = 1 and y = 5 is
1
5 .
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(9) 1
9
Step 1
Rules of the exponent:Rule 1: When we multiply any two numbers with the same base, we add the exponents.Rule 2: When we divide any two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we can multiply theexponent and the power.
Rule 4: (x)-n can be written as 1
(x)n
Step 2
Now, [ { (- 1
3 )1}-1]-2 can be simplified as:
= { (- 1
3 )1} -1 × -2
={ (- 1
3 )1}2
= (- 1
3 ) 1 × 2
=(- 1
3 )2
= 1
9
Step 3
Hence, the value of [ { (- 1
3 )1}-1]-2 is
1
9 .
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(10) -1
Step 1
Rules of the exponent:Rule 1: When we multiply any two numbers with the same base, we add the exponents.Rule 2: When we divide any two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we can multiply theexponent and the power.
Rule 4: (x)-n can be written as 1
(x)n
Rule 5: If, (y)x = (y)10 then we can write x = 10.
Step 2
Now
{( 1
3 )-1}x =
1
3
⇒ ( 1
3 )-1 × x =
1
3
⇒ ( 1
3 )(-1)(x) = (
1
31 )
⇒ ( 1
3 )(-1)(x) = (
1
3 )1
Comparing both sides: ⇒ (-1)(x) = 1 ⇒ x = -1
Step 3
Hence, the value of x is -1 .
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(11) 65
1
Step 1
can be simplified as:
+
= (3)3
(3)3 +
(4)3
(1)3
= 27
27 +
64
1
= 65
1
Step 2
Hence, the simplest fraction form of is 65
1 .
(12) 2x
Step 1
According to the question, Ferran plants a dandelion on his 8 th birthday. The plant has onedandelion in the beginning and the number of dandelions doubles every week.
Hence, the total number of dandelions after x weeks will be 2x.
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(13) A) 32
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
32 × 324
98 × 32 × 278 × 99 can be simplified as:
32 × 324
98 × 32 × 278 × 99
= (3)2 × 324
(3 × 3)8 × (3)2 × (3 × 3 × 3)8 × (3 × 3)9
= (3)2 × 324
(32)8 × (3)2 × (33)8 × (32)9
=
3(2 + 24)
3(16 + 2 +
24)
× 3(18)
= 326
342 × 318
= 326 ÷ 342 × 318
= 3(26 - 42 + 18)
= 32
Step 3
Hence, the exponential form of 32 × 324
98 × 32 × 278 × 99 is 32.
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B) 353
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Hence, the exponential form of 34 × 36 × 33 × 34 × 35 × 36 × 276
32 × 273 × 99 is 353.
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C) 218
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
89
49 × 29 can be simplified as:
89
49 × 29
= (2 × 2 × 2)9
(2 × 2)9 × (2)9
= (23)9
(22)9 × (2)9
= 2(27)
2(18) × 2(9)
= 227
218 × 29
= 227 ÷ 218 × 29
= 2(27 - 18 + 9)
= 218
Step 3
Hence, the exponential form of 89
49 × 29 is 218.
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D) 32
Step 1
Rules of the exponent:Rule 1: When we multiply two numbers with the same base, we add the exponents.Rule 2: When we divide two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we canmultiply the exponent and the power.
Step 2
96 × 311
279 × 93 can be simplified as:
96 × 311
279 × 93
= (3 × 3)6 × 311
(3 × 3 × 3)9 × (3 × 3)3
= (32)6 × 311
(33)9 × (32)3
=
3(12 +
11)
3(27)
× 3(6)
= 323
327 × 36
= 323 ÷ 327 × 36
= 3(23 - 27 + 6)
= 32
Step 3
Hence, the exponential form of 96 × 311
279 × 93 is 32.
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(14) 1
Step 1
Rules of the exponent:Rule 1: When we multiply any two numbers with the same base, we add the exponents.Rule 2: When we divide any two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we can multiply theexponent and the power.
Rule 4: (x)-n can be written as 1
(x)n
Rule 5: If, (y)x = (y)10 then we can write x = 10.
Step 2
Now
[{( 1
2 )1}1]x =
1
2
⇒ {( 1
2 )1}1x =
1
(2)1
⇒ ( 1
2 )1x =
1
(2)1
⇒ ( 1
2 )1x = (
1
2 )1
⇒ 1x = 1⇒ x = 1
Step 3
Hence, the value of x is 1 .
ID : ae-7-Exponents-and-Powers [20]
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(15) 27
1000
Step 1
Remember the following rules of exponents:Rule 1: When we multiply any two numbers with the same base, we add the exponents.Rule 2: When we divide any two numbers with the same base, we subtract the exponents.Rule 3: When we have an exponent expression that is raised to a power, we can multiply theexponent and the power.
Rule 4: (x)-n can be written as 1
(x)n
Step 2
Now can be simplified as:
=
1
=
1
(5)3
(3)3 ÷
(2)3
(4)3
=
1
125
27 ÷
8
64
=
1
125
27 ×
64
8
=
1
8000
216
= 27
1000
Step 3
Hence, the value of is 27
1000 .
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