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Indices and Surds

Year 10 · Number and Algebra · 100 questions · 60 min

Hard
0 of 100
Question 1

Simplify: 32^(3/5)

A fraction bar split into 5 equal parts with 3 shaded.3 out of 5 equal parts3/5
3/5 means 3 out of 5 equal parts.
Question 2

Evaluate: 27^(-2/3)

A fraction bar split into 3 equal parts with 2 shaded.2 out of 3 equal parts2/3
2/3 means 2 out of 3 equal parts.
Question 3

Express 5√2 / √8 in simplest form

Question 4

Rationalise the denominator: 3/(2√3)

A fraction bar split into equal parts.
Fractions compare selected parts with the total number of equal parts.
Question 5

Simplify: √(72) - √(8) + √(18)

Question 6

If 2^x = 16, find x

Question 7

Simplify: (x^(-2) × y^3)/(x × y^(-1))

Question 8

Express in exponential form: log₂(32) = 5

Question 9

Rationalise: (√5 + √2)/(√5 - √2)

Question 10

If √(2x + 7) = 5, find x

Question 11

Simplify: (8^(2/3) × 4^(-1/2))

A fraction bar split into 3 equal parts with 2 shaded.2 out of 3 equal parts2/3
2/3 means 2 out of 3 equal parts.
Question 12

Which expression equals 2^10?

Question 13

Simplify: ∛(54) + ∛(16) - ∛(2)

Question 14

Solve: 3^(2x) = 27

Question 15

Express without negative indices: (a^(-3) × b^2)/(c^(-1))

Question 16

Rationalise: 1/(3 + √5)

Question 17

Simplify: √(3) × √(12) × √(2)

Question 18

If log₃(x) = 4, find x

Question 19

Simplify: (16^(1/2) × 8^(1/3))/(2^(1/2))

A fraction bar split into 2 equal parts with 1 shaded.1 out of 2 equal parts1/2
1/2 means 1 out of 2 equal parts.
Question 20

Evaluate: (25^(-1/2) × 125^(2/3))

A fraction bar split into 2 equal parts with 1 shaded.1 out of 2 equal parts1/2
1/2 means 1 out of 2 equal parts.
Question 21

Simplify: 4^5 × 4^5

An array with 5 rows and 4 columns.5 rows x 4 columns = 20
Equal groups can be drawn as an array: 5 x 4.
Question 22

Simplify: (4^4)^4

Question 23

Practice card 3: Evaluate 3^3.

Question 24

Simplify: 5^4 ÷ 5^3

Question 25

Simplify: 8^4 × 8^4

An array with 4 rows and 8 columns.4 rows x 8 columns = 32
Equal groups can be drawn as an array: 4 x 8.
Question 26

Simplify: (7^6)^4

Question 27

Practice card 2: Simplify: (5^3)^5

Question 28

Practice card 3: Evaluate 2^2.

Question 29

Simplify: 7^4 ÷ 7^2

Question 30

Simplify: 2^5 × 2^6

An array with 5 rows and 2 columns.5 rows x 2 columns = 10
Equal groups can be drawn as an array: 5 x 2.
Question 31

Simplify: (9^2)^6

Question 32

Simplify: 8^6 × 8^5

An array with 6 rows and 8 columns.6 rows x 8 columns = 48
Equal groups can be drawn as an array: 6 x 8.
Question 33

Simplify: (2^6)^2

Question 34

Practice card 2: 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 35

Practice card 2: Evaluate 2^4.

Question 36

Simplify: 3^2 × 3^5

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 37

Simplify: (3^6)^3

Question 38

Practice card 3: Evaluate 4^2.

Question 39

Practice card 3: Evaluate 2^3.

Question 40

Practice card 3: Evaluate 5^2.

Question 41

Practice card 3: Evaluate 4^4.

Question 42

Practice card 3: Simplify: 3^6 ÷ 3^5

Question 43

Simplify: (4^2)^2

Question 44

Practice card 2: Simplify: 3^5 ÷ 3^2

Question 45

Simplify: (5^2)^5

Question 46

Practice card 3: Evaluate 3^2.

Question 47

Practice card 3: Simplify: (9^2)^5

Question 48

Practice card 2: Simplify: 3^6 ÷ 3^2

Question 49

Simplify: 8^3 × 8^3

An array with 3 rows and 8 columns.3 rows x 8 columns = 24
Equal groups can be drawn as an array: 3 x 8.
Question 50

Simplify: 9^3 × 9^4

An array with 3 rows and 9 columns.3 rows x 9 columns = 27
Equal groups can be drawn as an array: 3 x 9.
Question 51

Practice card 2: Simplify: 6^6 ÷ 6^5

Question 52

Simplify: (6^6)^6

Question 53

Simplify: 8^3 × 8^6

An array with 3 rows and 8 columns.3 rows x 8 columns = 24
Equal groups can be drawn as an array: 3 x 8.
Question 54

Practice card 3: Evaluate 3^4.

Question 55

Simplify: 2^3 × 2^5

An array with 3 rows and 2 columns.3 rows x 2 columns = 6
Equal groups can be drawn as an array: 3 x 2.
Question 56

Practice card 3: Evaluate 4^3.

Question 57

Simplify: (5^4)^4

Question 58

Practice card 3: Simplify: 2^4 ÷ 2^3

Question 59

Simplify: (8^3)^6

Question 60

Simplify: 4^6 × 4^6

An array with 6 rows and 4 columns.6 rows x 4 columns = 24
Equal groups can be drawn as an array: 6 x 4.
Question 61

Simplify: (7^5)^3

Question 62

Simplify: 9^5 × 9^5

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 63

Simplify: (2^6)^5

Question 64

Simplify: 8^5 × 8^5

An array with 5 rows and 8 columns.5 rows x 8 columns = 40
Equal groups can be drawn as an array: 5 x 8.
Question 65

Simplify: 9^5 ÷ 9^2

Question 66

Simplify: 7^5 ÷ 7^3

Question 67

Practice card 2: 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 68

Simplify: (5^6)^2

Question 69

Simplify: 6^4 × 6^2

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 70

Practice card 3: Evaluate 5^4.

Question 71

Simplify: 8^4 × 8^2

An array with 4 rows and 8 columns.4 rows x 8 columns = 32
Equal groups can be drawn as an array: 4 x 8.
Question 72

Practice card 2: Simplify: (2^3)^5

Question 73

Simplify: 5^2 × 5^3

An array with 2 rows and 5 columns.2 rows x 5 columns = 10
Equal groups can be drawn as an array: 2 x 5.
Question 74

Simplify: (9^3)^6

Question 75

Practice card 2: Simplify: 2^3 ÷ 2^2

Question 76

Simplify: 2^3 × 2^4

An array with 3 rows and 2 columns.3 rows x 2 columns = 6
Equal groups can be drawn as an array: 3 x 2.
Question 77

Simplify: 5^6 × 5^2

An array with 6 rows and 5 columns.6 rows x 5 columns = 30
Equal groups can be drawn as an array: 6 x 5.
Question 78

Simplify: (3^3)^4

Question 79

Simplify: 8^4 ÷ 8^3

Question 80

Simplify: 6^2 × 6^4

An array with 2 rows and 6 columns.2 rows x 6 columns = 12
Equal groups can be drawn as an array: 2 x 6.
Question 81

Practice card 2: Simplify: 5^4 ÷ 5^2

Question 82

Practice card 2: Simplify: 4^4 ÷ 4^3

Question 83

Simplify: 8^6 ÷ 8^5

Question 84

Simplify: 7^5 × 7^4

An array with 5 rows and 7 columns.5 rows x 7 columns = 35
Equal groups can be drawn as an array: 5 x 7.
Question 85

Practice card 2: Simplify: 9^5 ÷ 9^3

Question 86

Simplify: 6^2 × 6^3

An array with 2 rows and 6 columns.2 rows x 6 columns = 12
Equal groups can be drawn as an array: 2 x 6.
Question 87

Simplify: 4^4 × 4^5

An array with 4 rows and 4 columns.4 rows x 4 columns = 16
Equal groups can be drawn as an array: 4 x 4.
Question 88

Simplify: 5^5 × 5^2

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 89

Simplify: (7^5)^5

Question 90

Simplify: 7^4 ÷ 7^3

Question 91

Practice card 2: Simplify: (6^3)^6

Question 92

Simplify: (5^3)^4

Question 93

Practice card 2: Simplify: 7^5 ÷ 7^4

Question 94

Practice card 2: 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 95

Simplify: 6^6 × 6^6

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 96

Simplify: (3^5)^4

Question 97

Simplify: (8^3)^4

Question 98

Simplify: 5^6 ÷ 5^4

Question 99

Simplify: 8^4 ÷ 8^4

Question 100

Simplify: (3^6)^4

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