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Index Laws and Exponents

Year 8 · Number and Algebra · 100 questions · 60 min

Hard
0 of 100
Question 1

Simplify: 3^4 × 3^5 ÷ 3^6

An array with 4 rows and 3 columns.4 rows x 3 columns = 12
Equal groups can be drawn as an array: 4 x 3.
Question 2

Evaluate: (2^3)^2 × 2^-4

An array with 2 rows and 2 columns.2 rows x 2 columns = 4
Equal groups can be drawn as an array: 2 x 2.
Question 3

Simplify: 5^0 + 6^0 - 7^0

Question 4

If 2^x = 32, find the value of x.

Question 5

Simplify: (4^2 × 4^3) ÷ 4^4

An array with 2 rows and 4 columns.2 rows x 4 columns = 8
Equal groups can be drawn as an array: 2 x 4.
Question 6

Express 2^-3 as a fraction.

A fraction bar split into equal parts.
Fractions compare selected parts with the total number of equal parts.
Question 7

Simplify: (x^2 × x^4) ÷ x^5

Question 8

Evaluate: 3^2 + 2^3 - 4^2

Question 9

If 5^y = 125, what is y?

Question 10

Simplify: (6^2)^2 ÷ 6^3

Question 11

Calculate: (10^2)^-1

Question 12

Simplify: 2^5 × 3^2 ÷ 2^3 ÷ 3^1

An array with 5 rows and 3 columns.5 rows x 3 columns = 15
Equal groups can be drawn as an array: 5 x 3.
Question 13

What is the value of 7^1 - 7^0?

Question 14

Solve: 2^x × 2^3 = 2^8

Question 15

Evaluate: 4^2 ÷ 4^-1

Question 16

Simplify: (3^2 × 2^3) ÷ (3 × 2^2)

An array with 2 rows and 2 columns.2 rows x 2 columns = 4
Equal groups can be drawn as an array: 2 x 2.
Question 17

If 10^m = 0.001, find m.

Question 18

Simplify: (5^4)^2 ÷ 5^5

Question 19

Calculate: (2 × 3)^2

An array with 2 rows and 3 columns.2 rows x 3 columns = 6
Equal groups can be drawn as an array: 2 x 3.
Question 20

Evaluate: 8^(1/3)

A fraction bar split into 3 equal parts with 1 shaded.1 out of 3 equal parts1/3
1/3 means 1 out of 3 equal parts.
Question 21

Evaluate 5^3.

Question 22

Simplify: (9^3)^2

Question 23

Simplify: 9^2 × 9^2

An array with 2 rows and 9 columns.2 rows x 9 columns = 18
Equal groups can be drawn as an array: 2 x 9.
Question 24

Simplify: 3^5 × 3^3

An array with 5 rows and 3 columns.5 rows x 3 columns = 15
Equal groups can be drawn as an array: 5 x 3.
Question 25

Simplify: 4^6 ÷ 4^5

Question 26

Simplify: 7^6 × 7^5

An array with 6 rows and 7 columns.6 rows x 7 columns = 42
Equal groups can be drawn as an array: 6 x 7.
Question 27

Simplify: 5^5 × 5^4

An array with 5 rows and 5 columns.5 rows x 5 columns = 25
Equal groups can be drawn as an array: 5 x 5.
Question 28

Simplify: 7^3 ÷ 7^3

Question 29

Simplify: 9^6 ÷ 9^5

Question 30

Simplify: (9^2)^5

Question 31

Simplify: (3^3)^5

Question 32

Simplify: 9^4 ÷ 9^2

Question 33

Simplify: 2^2 × 2^2

An array with 2 rows and 2 columns.2 rows x 2 columns = 4
Equal groups can be drawn as an array: 2 x 2.
Question 34

Simplify: 2^6 ÷ 2^4

Question 35

Simplify: 5^3 ÷ 5^2

Question 36

Simplify: 3^6 ÷ 3^2

Question 37

Simplify: 5^4 × 5^2

An array with 4 rows and 5 columns.4 rows x 5 columns = 20
Equal groups can be drawn as an array: 4 x 5.
Question 38

Evaluate 4^4.

Question 39

Simplify: 8^5 ÷ 8^3

Question 40

Evaluate 3^3.

Question 41

Simplify: 7^2 × 7^5

An array with 2 rows and 7 columns.2 rows x 7 columns = 14
Equal groups can be drawn as an array: 2 x 7.
Question 42

Simplify: 7^2 × 7^6

An array with 2 rows and 7 columns.2 rows x 7 columns = 14
Equal groups can be drawn as an array: 2 x 7.
Question 43

Simplify: 3^6 ÷ 3^4

Question 44

Evaluate 4^2.

Question 45

Evaluate 5^4.

Question 46

Simplify: 6^3 × 6^5

An array with 3 rows and 6 columns.3 rows x 6 columns = 18
Equal groups can be drawn as an array: 3 x 6.
Question 47

Simplify: (4^6)^6

Question 48

Simplify: 6^6 × 6^3

An array with 6 rows and 6 columns.6 rows x 6 columns = 36
Equal groups can be drawn as an array: 6 x 6.
Question 49

Simplify: (2^3)^5

Question 50

Evaluate 2^3.

Question 51

Simplify: 4^2 × 4^5

An array with 2 rows and 4 columns.2 rows x 4 columns = 8
Equal groups can be drawn as an array: 2 x 4.
Question 52

Evaluate 2^2.

Question 53

Simplify: 7^3 × 7^5

An array with 3 rows and 7 columns.3 rows x 7 columns = 21
Equal groups can be drawn as an array: 3 x 7.
Question 54

Simplify: 5^5 ÷ 5^4

Question 55

Simplify: (6^2)^3

Question 56

Simplify: 5^4 ÷ 5^2

Question 57

Simplify: 9^6 ÷ 9^2

Question 58

Simplify: (4^5)^5

Question 59

Simplify: 6^6 ÷ 6^5

Question 60

Simplify: 9^5 ÷ 9^3

Question 61

Simplify: (4^6)^3

Question 62

Simplify: 4^2 × 4^2

An array with 2 rows and 4 columns.2 rows x 4 columns = 8
Equal groups can be drawn as an array: 2 x 4.
Question 63

Simplify: 6^4 × 6^6

An array with 4 rows and 6 columns.4 rows x 6 columns = 24
Equal groups can be drawn as an array: 4 x 6.
Question 64

Simplify: (6^6)^4

Question 65

Evaluate 4^3.

Question 66

Simplify: 7^2 × 7^3

An array with 2 rows and 7 columns.2 rows x 7 columns = 14
Equal groups can be drawn as an array: 2 x 7.
Question 67

Simplify: 9^4 × 9^2

An array with 4 rows and 9 columns.4 rows x 9 columns = 36
Equal groups can be drawn as an array: 4 x 9.
Question 68

Simplify: 2^5 ÷ 2^4

Question 69

Simplify: 3^5 ÷ 3^3

Question 70

Simplify: 4^5 ÷ 4^3

Question 71

Simplify: 9^5 × 9^3

An array with 5 rows and 9 columns.5 rows x 9 columns = 45
Equal groups can be drawn as an array: 5 x 9.
Question 72

Simplify: 3^5 × 3^6

An array with 5 rows and 3 columns.5 rows x 3 columns = 15
Equal groups can be drawn as an array: 5 x 3.
Question 73

Simplify: 6^4 ÷ 6^2

Question 74

Simplify: (3^4)^5

Question 75

Simplify: (3^3)^6

Question 76

Simplify: 7^5 ÷ 7^4

Question 77

Simplify: 3^5 × 3^2

An array with 5 rows and 3 columns.5 rows x 3 columns = 15
Equal groups can be drawn as an array: 5 x 3.
Question 78

Simplify: 6^4 ÷ 6^3

Question 79

Evaluate 3^2.

Question 80

Evaluate 3^4.

Question 81

Simplify: (5^6)^4

Question 82

Simplify: 3^6 ÷ 3^5

Question 83

Simplify: 6^5 × 6^6

An array with 5 rows and 6 columns.5 rows x 6 columns = 30
Equal groups can be drawn as an array: 5 x 6.
Question 84

Simplify: 2^4 ÷ 2^3

Question 85

Evaluate 5^2.

Question 86

Simplify: (6^3)^3

Question 87

Simplify: 4^4 ÷ 4^2

Question 88

Simplify: (2^6)^6

Question 89

Simplify: 2^6 × 2^5

An array with 6 rows and 2 columns.6 rows x 2 columns = 12
Equal groups can be drawn as an array: 6 x 2.
Question 90

Simplify: 3^3 × 3^6

An array with 3 rows and 3 columns.3 rows x 3 columns = 9
Equal groups can be drawn as an array: 3 x 3.
Question 91

Simplify: (2^6)^4

Question 92

Simplify: (7^4)^4

Question 93

Simplify: 4^2 × 4^6

An array with 2 rows and 4 columns.2 rows x 4 columns = 8
Equal groups can be drawn as an array: 2 x 4.
Question 94

Simplify: 2^2 ÷ 2^2

Question 95

Simplify: 3^2 ÷ 3^2

Question 96

Simplify: (2^5)^5

Question 97

Simplify: 3^5 ÷ 3^2

Question 98

Simplify: (5^4)^6

Question 99

Simplify: 5^6 ÷ 5^2

Question 100

Simplify: (9^6)^5

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