# Spectrum Math Grade 8 Chapter 1 Lesson 2 Answer Key Equivalent Expressions with Exponents

Students can use the Spectrum Math Grade 8 Answer Key Chapter 1 Lesson 1.2 Equivalent Expressions with Exponents as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 1 Lesson 1.2 Equivalent Expressions with Exponents Answers Key

To multiply powers with the same base, combine bases, add the exponents, then simplify.
22 × 23 = 22 + 3 = 25 = 32
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
35 ÷ 32 = 35 – 2 = 33 = 27

Find the value of each expression.

Question 1.
a. 72 = ____
A power of a number represents repeated multiplication of the number by itself.
72 =7 x 7 and is read 7 to the second 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 factor. In 72, 7 is the base and 2 is the exponent.
72 means 7 is used as a factor 2 times.
7 x 7 = 72
7 x 7 = 49
72 = 49

b. 83 = ____
A power of a number represents repeated multiplication of the number by itself.
83 = 8 x 8 x 8  and is read 8 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 factor. In 83 , 8 is the base and 3 is the exponent.
83 means 8 is used as a factor 3 times.
8 x 8 x 8  = 83
8 x 8 x 8  = 512
83 = 512

c. 43 = _____
A power of a number represents repeated multiplication of the number by itself.
43 = 4 x 4  x 4   and is read 4 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 factor. In 43, 4 is the base and 3 is the exponent.
43 means 4 is used as a factor 3 times.
4 x 4  x 4  = 43
4 x 4  x 4  = 64
43 = 64

Question 2.
a. 102 = ____
A power of a number represents repeated multiplication of the number by itself.
102 =10 x 10 and is read 10 to the second 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 factor. In 102 , 10 is the base and 2 is the exponent.
102 means 10 is used as a factor 2 times.
10 x 10 = 102
10 x 10 = 100
102 = 100

b. 94 = ____
A power of a number represents repeated multiplication of the number by itself.
94 = 9 x 9 x 9 x 9 and is read 9 to the fourth 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 factor. In 94, 9 is the base and 4 is the exponent.
94 means 9 is used as a factor 4 times.
9 x 9 x 9 x 9  = 94
9 x 9 x 9 x 9 = 6561
94 = 6561

c. 115 = _____
A power of a number represents repeated multiplication of the number by itself.
115 = 11 x 11 x 11 x 11 x 11 and is read 11 to the fifth 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 factor. In 115, 11 is the base and 5 is the exponent.
115 means 11 is used as a factor 5 times.
11 x 11 x 11 x 11 x 11 = 115
11 x 11 x 11 x 11 x 11 = 161051
115 = 161051

Question 3.
a. 173 = ____
A power of a number represents repeated multiplication of the number by itself.
173 = 17 x 17 x 17  and is read 17 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 factor. In 173, 17 is the base and 3 is the exponent.
173 means 17 is used as a factor 3 times.
17 x 17 x 17 = 173
17 x 17 x 17 = 4913
173 = 4913

b. 56 = ____
A power of a number represents repeated multiplication of the number by itself.
56 = 5 × 5 × 5 × 5 × 5 × 5 and is read 5 to the sixth 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 factor. In 56, 5 is the base and 6 is the exponent.
56 means 5 is used as a factor 6 times.
5 × 5 × 5 × 5 × 5 × 5 = 56
5 × 5 × 5 × 5 × 5 × 5 = 15625
56 = 15625

c. 64 = _____
A power of a number represents repeated multiplication of the number by itself.
64 = 6 × 6 × 6 × 6 and is read 6 to the fourth 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 factor. In 64, 6 is the base and 4 is the exponent.
64 means 6 is used as a factor 4 times.
6 × 6 × 6 × 6 = 64
6 × 6 × 6 × 6 = 1296
6= 1296

Question 4.
a. 213 = ____
A power of a number represents repeated multiplication of the number by itself.
213 = 21 x 21 x 21 and is read 21 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 factor. In 213, 21 is the base and 3 is the exponent.
213 means 21 is used as a factor 3 times.
21 x 21 x 21 = 213
21 x 21 x 21 = 9261
213 = 9261

b. 164 = ____
A power of a number represents repeated multiplication of the number by itself.
164 = 16 × 16 × 16 × 16 and is read 16 to the fourth 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 factor. In 164, 16 is the base and 4 is the exponent.
164 means 16 is used as a factor 4 times.
16 × 16 × 16 × 16 = 64
16 × 16 × 16 × 16 = 65536
6= 65536

c. 125 = _____
A power of a number represents repeated multiplication of the number by itself.
125 = 12 x 12 x 12 x 12 x 12 and is read 12 to the fifth 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 factor. In 125, 12 is the base and 5 is the exponent.
125 means 11 is used as a factor 5 times.
12 x 12 x 12 x 12 x 12 = 125
12 x 12 x 12 x 12 x 12 = 248832
125 = 248832

Rewrite each expression as one base and one exponent. Then, find the value.

Question 5.
a. 82 × 83 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
82 × 83 = 82 + 3 = 85 = 32768

b. 33 × 33 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
33 × 33 = 33 + 3 = 36 = 729

c. 22 × 22 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
22 × 22 = 22 + 2 = 24 = 16

Question 6.
a. 74 ÷ 72 = ___
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
74 ÷ 72 = 74 – 2 = 72 = 49

b. 95 ÷ 93 = ___
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
95 ÷ 93 = 95 – 3 = 92 = 81

c. 164 ÷ 162 = ___
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
164 ÷ 162 = 164 – 2 = 162 = 256

Question 7.
a. 64 × 61 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
64 × 61 = 64 + 1 = 65 = 7776

b. 44 × 42 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
44 × 4 = 44 + 2 = 46 = 4096

c. 32 × 32 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
32 × 32 = 32 + 2 = 34 = 81

Question 8.
a. 106 ÷ 104 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
106 ÷ 104 = 106 – 4 = 102 = 100

b. 83 ÷ 82 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
83 ÷ 82 = 83 – 2 = 81 = 8

c. 76 ÷ 73 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
76 ÷ 73 = 76 – 3 = 73 = 343

Question 9.
a. 53 × 52 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
53 × 52 = 53 + 2 = 55 = 3125

b. 103 × 104 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
103 × 104 = 103 + 4 = 107 = 10000000

c. 152 × 151 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
152 × 151= 152 + 1 = 153 = 3375

d. 66 ÷ 63 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
66 ÷ 63 = 66 – 3 = 63 = 216

Rewrite each multiplication or division expression using a base and an exponent.

Question 1.
a. 43 × 45 = _____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
43 × 45= 43 + 5 = 48 = 65536

b. 92 × 93 = _____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
92 × 93 = 92 + 3 = 95 = 59049

Question 2.
a. (3 × 3 × 3) × (3 × 3) = _______
33 + 2  = 35 = 243
To multiply powers with the same base, combine bases, add the exponents, then simplify.
(3 × 3 × 3) × (3 × 3) = 33 × 32 = 33 + 2 = 35 = 243

b. 56 ÷ 53 = _______
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
56 ÷ 53  = 56 – 3 = 53 =  125

Question 3.
a. 85 ÷ 8 = _______
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
85 ÷ 8 = 85 – 1 = 84 = 4096

b. (2 × 2 × 2 × 2) ÷ (2 × 2) = _______
24 + 2  = 26 = 64
To multiply powers with the same base, combine bases, add the exponents, then simplify.
(2 × 2 × 2 × 2) ÷ (2 × 2) = 24 × 22 = 24 + 2 = 26 = 64

Question 4.
a. (5 × 5) × (5 × 5) = ______
52 + 2  = 54 = 625
To multiply powers with the same base, combine bases, add the exponents, then simplify.
(5 × 5) × (5 × 5)= 52 × 52 = 52 + 2  = 54 = 625

b. 99 ÷ 95 = _______
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
99 ÷ 95 = 99 – 5 = 94 = 6561

Question 5.
a. 103 × 10 = ______
To multiply powers with the same base, combine bases, add the exponents, then simplify.
103 × 10 = 103 + 1 = 104 = 1000

b. 65 ÷ 62 = _______
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
65 ÷ 62 = 65 – 2 = 63 = 216

Question 6.
a. 43 ÷ 42 = _______
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
43 ÷ 42 = 43 – 2 = 41 = 4

b. (7 × 7 × 7) ÷ 7 = _______
73 – 1  = 72 = 49
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
(7 × 7 × 7) ÷ 7 =73 ÷ 71= 73 – 1  = 72 = 49

Question 7.
a. 115 × 112 = _______
To multiply powers with the same base, combine bases, add the exponents, then simplify.
115 × 112 = 115 + 2 = 117 = 19487171

b. 6 × 65 = _______
To multiply powers with the same base, combine bases, add the exponents, then simplify.
6 × 65 = 61 + 5 = 66 = 46656

Question 8.
a. (8 × 8 × 8 × 8) ÷ (8 × 8) = _____
84- 2  = 82 =  64
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
(8 × 8 × 8 × 8) ÷ (8 × 8) =84 ÷ 82  =84- 2  = 82 =  64

b. 53 × 52 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
53 × 52 = 53 + 2 = 55 = 3125

Question 9.
a. 129 × 122 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
129 × 122 = 129 + 2 = 1211 = 743008370688

b. 1110 ÷ 114 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
1110 ÷ 114 = 1110 – 4 = 116 = 1771561

Question 10.
a. 34 × 34 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
34 × 34 = 34 + 4 = 38 = 6561

b. (4 × 4 × 4 × 4) ÷ 4 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
(4 × 4 × 4 × 4) ÷ 4  = 44 ÷ 41 = 44 – 1 = 43 = 64

Question 11.
a. (5 × 5 × 5) ÷ 5 = _____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
(5 × 5 × 5) ÷ 5 =53 ÷ 51  =53- 1  = 52 = 25

b. 68 × 64 = _____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
68 × 64 = 68 + 4 = 612 = 2176782336

Question 12.
a. 412 ÷ 46 = ____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
412 ÷ 46 = 412- 6  = 46 = 4096

b. 33 × 39 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
33 × 39 = 33 + 9 = 312 = 531441

Question 13.
a. (6 × 6 × 6 × 6) ÷ (6 × 6 × 6) = _____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
(6 × 6 × 6 × 6) ÷ (6 × 6 × 6) = 64 ÷ 63 = 64 – 3 = 61 = 6

b. 158 ÷ 153 = _____
To divide powers with the same base, combine bases, subtract the exponents, then simplify.
158 ÷ 153 = 158 – 3 = 155 = 759375

Question 14.
a. 99 × 96 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
99 × 96 = 99 + 6 = 915 = 205891132094649

b. 78 × 72 = ____
To multiply powers with the same base, combine bases, add the exponents, then simplify.
78 × 72 = 78 + 2 = 710 = 282475249

Question 15.
a. 27 ÷ 2 = ____