Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.1 Using Exponents and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 5 Lesson 5.1 Using Exponents Answers Key
A power of a number represents repeated multiplication of the number by itself.
103 = 10 × 10 × 10 and is read 10 to the third power.
In exponential numbers, the base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In 25, 2 is the base and 5 is the exponent.
25 means 2 is used as a factor 5 times.
2 × 2 × 2 × 2 × 2 = 32 25 = 32
Scientific notation for a number is expressed by writing the number as the product of a number between one and ten, and a power of ten.
3,000 can be written as 3 × 1,000 or 3 × 103.
3 × 103 is scientific notation for 3,000.
Some powers of 10 are shown in the table at right.
Use the table above to write each number in scientific notation.
Question 1.
a. 30 ______
Answer:
The given number in Scientific notation can be written as 3 x 101
b. 4,000 ______
Answer:
The given number in Scientific notation can be written as 4 x 103
c. 50,000 _____
Answer:
The given number in Scientific notation can be written as 5 x 104
Question 2.
a. 600,000 ____
Answer:
The given number in Scientific notation can be written as 6 x 105
b. 700 ____
Answer:
The given number in Scientific notation can be written as 7 x 102
c. 90 _____
Answer:
The given number in Scientific notation can be written as 9 x 101
Question 3.
a. 40,000 ____
Answer:
The given number in Scientific notation can be written as 4 x 104
b. 100,000 ____
Answer:
The given number in Scientific notation can be written as 1 x 105
c. 400 ____
Answer:
The given number in Scientific notation can be written as 4 x 102
Write each power as the product of factors.
Question 4.
a. 33 ______
Answer:
Given value is 33
It can be written as a product of 3 x 3 x 3
= 27
Therefore the value of 33 is 27.
b. 55 ______
Answer:
Given value is 55
It can be written as a product of 5 x 5 x 5
=125
Therefore the value of 55 is 125 .
c. 16 ______
Answer:
Given value is 16
It can be written as a product of 1 x 1 x 1 x 1 x 1 x 1
=1
Therefore the value of 16 is 1.
Question 5.
a. 122 ______
Answer:
Given value is 122
It can be written as a product of 12 x 12
=144
Therefore the value of 122 is 144.
b. 83 ______
Answer:
Given value is 83
It can be written as a product of 8 x 8 x 8
=512
Therefore the value of 83 is 512 .
c. 63 ______
Answer:
Given value is 63
It can be written as a product of 6 x 6 x 6
=216
Therefore the value of 63 is 216 .
Question 6.
a. 74 ______
Answer:
Given value is 74
It can be written as a product of 7 x 7 x 7 x 7
=2401
Therefore the value of 74 is 2401.
b. 44 ______
Answer:
Given value is 44
It can be written as a product of 4 x 4 x 4 x 4
= 256
Therefore the value of 44 is 256 .
c. 114 ______
Answer:
Given value is 114
It can be written as a product of 11 x 11 x 11 x 11
= 14641
Therefore the value of 114 is 14641.
Use exponents to rewrite each expression.
Question 7.
a. 3 × 3 × 3 ____
Answer:
Given 3 x 3 x 3
It can be written as a 33
= 27
Therefore the value of 3 x 3 x 3 is 33 which is equal to 27.
b. 8 × 8 _____
Answer:
Given 8 x 8
It can be written as 82
= 64
Therefore the value of 8x 8 is 82 which is equal to 64.
c. 7 × 7 × 7 × 7 × 7 _____
Answer:
Given 7 × 7 × 7 × 7 × 7
It can be written as 75
= 16,807
Therefore the value of 7 × 7 × 7 × 7 × 7 is 75 which is equal to 16,807.
Question 8.
a. 24 × 24 _____
Answer:
Given 24 × 24
It can be written as 242
= 576
Therefore the value of 24 × 24 is 242 which is equal to 576.
b. 4 × 4 × 4 _____
Answer:
Given 4 × 4 x 4
It can be written as 4 3
= 64
Therefore the value of 24 × 24 is 4 3 which is equal to 64.
c. 6 × 6 × 6 × 6 × 6 × 6 _____
Answer:
Given 6 × 6 × 6 × 6 × 6 × 6
It can be written as 66
=46,656
Therefore the value of 6 × 6 × 6 × 6 × 6 × 6 is 66 which is equal to 46,656 .
Question 9.
a. 2 × 2 × 2 × 2 ____
Answer:
Given 2 × 2 × 2 × 2
It can be written as 24
= 16
Therefore the value of 2 × 2 × 2 × 2 is 24 which is equal to 16.
b. 38 × 38 × 38 _____
Answer:
Given 38 × 38 × 38
It can be written as 383
= 54,872
Therefore the value of 38 x 38 x38 is 383 which is equal to 54,872.
c. 5 × 5 × 5 × 5 × 5 _____
Answer:
Given 5 × 5 × 5 × 5 × 5
It can be written as 55
= 3125
Therefore the value of 5 x 5 x 5 x 5 x 5 is 55 which is equal to 3125.
Question 10.
a. a4 if a = 2 ____
Answer:
Given Expression a4
By Substituting the given value a = 2, the Expression becomes as shown Below
a4 = 14
= 1 x 1 x 1 x 1
= 1
Therefore the value of a = 1
b. x3 if x = 4 ____
Answer:
Given Expression x3
By Substituting the given value x = 4, the Expression becomes as shown Below
x3 = 43
= 4 x 4 x 4
= 64
Therefore the value of x is 64
c. n7 if n = 1 ____
Answer:
Given Expression n7
By Substituting the given value n = 1, the Expression becomes as shown Below
n7 = 17
= 1 x 1 x1 x 1 x 1 x 1 x 1
= 1
Therefore the value of n is 1.
Question 11.
a. n2 if n = 8 ____
Answer:
Given Expression n2
By Substituting the given value n =81, the Expression becomes as shown Below
n2 = 82
= 8 x 8
= 64
Therefore the value of n is 64.
b. b4 if b = 3 ____
Answer:
Given Expression b4
By Substituting the given value n =81, the Expression becomes as shown Below
b4 = 34
= 3 x 3 x 3 x 3
= 81
Therefore the value of b is 81.
c. x3 if x = 5 _____
Answer:
Given Expression x3
By Substituting the given value x =5, the Expression becomes as shown Below
x3 = 53
= 5 x 5 x 5
= 125
Therefore the value of x is 125.
Question 12.
a. a5 if a = 3 ____
Answer:
Given Expression a 5
By Substituting the given value a =3, the Expression becomes as shown Below
a 5 = 35
= 3 x 3 x 3 x 3 x 3
= 243
Therefore the value of a is 243.
b. x3 if x = 6 ____
Answer:
Given Expression x3
By Substituting the given value x = 6, the Expression becomes as shown Below
x 3 = 63
= 6 x 6 x 6
= 216
Therefore the value of x is 216.
c. n2 if n = 11 ____
Answer:
Given Expression n2
By Substituting the given value n = 11 , the Expression becomes as shown Below
n2 = 112
= 11 x 11
= 121
Therefore the value of n is 121.
Write each power as the product of factors.
Question 1.
a.
35 __________
Answer:
Given value is 35
It can be written as a product of 3 x 3 x 3 x 3 x 3
=243
Therefore the value of 35 is 243 .
b.
93 __________
Answer:
Given value is 93
It can be written as a product of 9 x 9 x 9
= 729
Therefore the value of 93 is 729.
c.
27 __________
Answer:
Given value is 27
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2
=128
Therefore the value of 27 is 128 .
Question 2.
a.
102 __________
Answer:
Given value is 102
It can be written as a product of 10 x 10
=100
Therefore the value of 102 is 100 .
b.
34 __________
Answer:
Given value is 34
It can be written as a product of 3 x 3 x 3 x 3
= 81
Therefore the value of 34 is 81.
c.
28 __________
Answer:
Given value is 28
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
Therefore the value of 28 is 256.
Question 3.
a.
73 __________
Answer:
Given value is 73
It can be written as a product of 7 x 7 x 7
= 343
Therefore the value of 73 is 343 .
b.
42 __________
Answer:
Given value is 42
It can be written as a product of 4 x 4
= 16
Therefore the value of 42 is 16 .
c.
72 __________
Answer:
Given value is 72
It can be written as a product of 7 x 7
= 49
Therefore the value of 72 is 49.
Question 4.
a.
93 __________
Answer:
Given value is 93
It can be written as a product of 9 x 9 x 9
= 729
Therefore the value of 93 is 729.
b.
81 __________
Answer:
Given value is 81
It can be written as a product of 8
= 8
Therefore the value of 81 is 8.
c.
122 __________
Answer:
Given value is 122
It can be written as a product of 12 x 12
= 144
Therefore the value of 122 is 144.
Question 5.
a.
54 __________
Answer:
Given value is 54
It can be written as a product of 5 x 5 x 5 x 5
= 625
Therefore the value of 54 is 625.
b.
113 __________
Answer:
Given value is 113
It can be written as a product of 11 x 11 x 11
= 1331
Therefore the value of 113 is 1331.
c.
65 __________
Answer:
Given value is 65
It can be written as a product of 6 x 6 x 6 x 6 x 6
= 7,776
Therefore the value of 65 is 7,776.
Question 6.
a.
44 __________
Answer:
Given value is 44
It can be written as a product of 4 x 4 x 4 x 4
= 256
Therefore the value of 44 is 256.
b.
103 __________
Answer:
Given value is 103
It can be written as a product of 10 x 10 x 10
= 1000
Therefore the value of 103 is 1000.
c.
86 __________
Answer:
Given value is 86
It can be written as a product of 8 x 8 x 8 x 8 x 8 x 8
= 2, 62,1 44
Therefore the value of 86 is 2,62,144.
Use exponents to rewrite each expression.
Question 7.
a. 3 × 3 × 3 = ____
Answer:
Given Expression 3 × 3 × 3
It can be written as 33
= 81
Therefore the value of 3 × 3 × 3 is 33 which is equal to 81.
b. 5 × 5 × 5 × 5 × 5 = ____
Answer:
Given Expression 5 × 5 × 5 × 5 × 5
It can be written as 55
=3125
Therefore the value of 5 × 5 × 5 × 5 × 5 is 55 which is equal to 3125.
c. 2 × 2 × 2 × 2 × 2 × 2 = _____
Answer:
Given Expression 2 × 2 × 2 × 2 × 2 × 2
It can be written as 26
= 64
Therefore the value of 2 × 2 × 2 × 2 × 2 × 2 is 26 which is equal to 64.
Question 8.
a. 9 × 9 × 9 = ____
Answer:
Given Expression 9 × 9 × 9
It can be written as 93
= 729
Therefore the value of 9 × 9 × 9 is 93 which is equal to 729.
b. 4 × 4 × 4 × 4 × 4 × 4 × 4 = ____
Answer:
Given Expression 4 × 4 × 4 × 4 × 4 × 4 × 4
It can be written as 47
=16384
Therefore the value of 4 × 4 × 4 × 4 × 4 × 4 × 4 is 47 which is equal to 16384.
c. 21 × 21 = ____
Answer:
Given Expression 21 x 21
It can be written as 212
= 441
Therefore the value of 21 x 21 is 212 which is equal to 441.
Question 9.
a. 10 × 10 × 10 × 10 = ____
Answer:
Given Expression 10 x 10 x 10 x 10
It can be written as 104
= 10,000
Therefore the value of 10 x 10 x 10 x 10 is 104 which is equal to 10,000.
b. 8 × 8 × 8 × 8 × 8 = ____
Answer:
Given Expression 8 × 8 × 8 × 8 × 8
It can be written as 85
= 32,768
Therefore the value of 8 × 8 × 8 × 8 × 8 is 85 which is equal to 32,768.
c. 7 × 7 × 7 × 7 = ____
Answer:
Given Expression 7 × 7 × 7 × 7
It can be written as 74
= 2,401
Therefore the value of 7 × 7 × 7 × 7 is 74 which is equal to 2401.
Evaluate each expression.
Question 10.
a. 85 _____
Answer:
Given value is 85
It can be written as a product of 8 x 8 x 8 x 8 x 8
= 32,768
Therefore the value of 85 is Equal to 32,768.
b. 28 _____
Answer:
Given value is 28
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
Therefore the value of 28 is Equal to 256.
c. 34 _____
Answer:
Given value is 34
It can be written as a product of 3 x 3 x 3 x 3
= 81
Therefore the value of 34 is Equal to 81.
Question 11.
a. 62 _____
Answer:
Given value is 62
It can be written as a product of 6 x 6
= 36
Therefore the value of 62 is Equal to 36.
b. 91 _____
Answer:
Given value is 91
It can be written as a product of 9
= 9
Therefore the value of 91 is Equal to 9.
c. 104 _____
Answer:
Given value is 104
It can be written as a product of 10 x 10 x 10 x 10
= 10, 000
Therefore the value of 104 is Equal to 10,000.
Question 12.
a. 44 _____
Answer:
Given value is 44
It can be written as a product of 4 x 4 x 4 x 4
= 256
Therefore the value of 44 is Equal to 256.
b. 74 _____
Answer:
Given value is 74
It can be written as a product of 7 x 7 x 7 x 7
= 2401
Therefore the value of 74 is Equal to 2401.
c. 122 _____
Answer:
Given value is 122
It can be written as a product of 12 x 12
= 144
Therefore the value of 122 is Equal to 144 .