# Spectrum Math Grade 6 Chapter 5 Lesson 1 Answer Key Using Exponents

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 ______
The given number in Scientific notation can be written as 3 x 101

b. 4,000 ______
The given number in Scientific notation can be written as 4 x 103

c. 50,000 _____
The given number in Scientific notation can be written as 5 x 104

Question 2.
a. 600,000 ____
The given number in Scientific notation can be written as 6 x 105

b. 700 ____
The given number in Scientific notation can be written as 7 x 102

c. 90 _____
The given number in Scientific notation can be written as 9 x 101

Question 3.
a. 40,000 ____
The given number in Scientific notation can be written as 4 x 104

b. 100,000 ____
The given number in Scientific notation can be written as 1 x 105

c. 400 ____
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 ______
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 ______
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 ______
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 ______
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 ______
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 ______
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 ______
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 ______
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 ______
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 ____
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 _____
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 _____
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 _____
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 _____
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 _____
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 ____
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 _____
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 _____
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 ____
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 ____
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 ____
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 ____
Given Expression  n2
By Substituting the given value n =81, the Expression becomes as shown Below
n= 82
= 8 x 8
= 64
Therefore the value of n is 64.

b. b4 if b = 3 ____
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 _____
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 ____
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 ____
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 ____
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 __________
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 __________
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 __________
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 __________
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 __________
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 __________
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 __________
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 __________
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 __________
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 __________
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 __________
Given value is 81
It can be written as a product of  8
= 8
Therefore the value of 81 is 8.

c.
122 __________
Given value is 122
It can be written as a product of  12 x 12
= 144
Therefore the value of 12 is 144.

Question 5.
a.
54 __________
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 __________
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 __________
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 __________
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 __________
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 __________
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 = ____
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 = ____
Given Expression 5 × 5 × 5 × 5 × 5
It can be written as  55
=3125
Therefore the value of 5 × 5 × 5 × 5 × 5  is 5 which is equal to 3125.

c. 2 × 2 × 2 × 2 × 2 × 2 = _____
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 = ____
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 = ____
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 = ____
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 = ____
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 = ____
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 = ____
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 _____
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 _____
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 _____
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 _____
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 _____
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 _____
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 _____
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 _____
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 _____