Indices and Surds

Question 1

Simplify: 32^(3/5)

A 6 B 8 C 16 D 32

Question 2

Evaluate: 27^(-2/3)

A 1/9 B 1/3 C -1/9 D -1/3

Question 3

Express 5√2 / √8 in simplest form

A 5√2/2 B 5/2 C 5√4 D 10

Question 4

Rationalise the denominator: 3/(2√3)

A √3/2 B 3√3/2 C √3 D 2√3

Question 5

Simplify: √(72) - √(8) + √(18)

A 4√2 B 7√2 C 8√2 D 10√2

Question 6

If 2^x = 16, find x

A 2 B 3 C 4 D 5

Question 7

Simplify: (x^(-2) × y^3)/(x × y^(-1))

A y^4/x^3 B x^3/y^4 C y^2/x^3 D x^3/y^2

Question 8

Express in exponential form: log₂(32) = 5

A 2^32 = 5 B 2^5 = 32 C 5^2 = 32 D 32^2 = 5

Question 9

Rationalise: (√5 + √2)/(√5 - √2)

A (7 + 2√10)/3 B (7 - 2√10)/3 C 5 + 2√10 D 7 + 2√10

Question 10

If √(2x + 7) = 5, find x

A 6 B 9 C 12 D 18

Question 11

Simplify: (8^(2/3) × 4^(-1/2))

A 1 B 2 C 4 D 8

Question 12

Which expression equals 2^10?

A 32 × 32 B 64 × 16 C 128 × 8 D 256 × 8

Question 13

Simplify: ∛(54) + ∛(16) - ∛(2)

A 3∛(2) B 4∛(2) C 5∛(2) D 6∛(2)

Question 14

Solve: 3^(2x) = 27

A 1.5 B 1.75 C 2 D 2.25

Question 15

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

A b^2c/a^3 B a^3/(b^2c) C c/(a^3b^2) D a^3b^2c

Question 16

Rationalise: 1/(3 + √5)

A (3 - √5)/4 B (3 + √5)/4 C (√5 - 3)/4 D 3/(9 - 5)

Question 17

Simplify: √(3) × √(12) × √(2)

A 6 B 6√2 C 12 D 12√2

Question 18

If log₃(x) = 4, find x

A 12 B 27 C 64 D 81

Question 19

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

A 4√2 B 8 C 16 D 32

Question 20

Evaluate: (25^(-1/2) × 125^(2/3))

A 5 B 15 C 20 D 25

Question 21

Evaluate 5^3.

A 125 B 120 C 130 D 15

Question 22

Evaluate 4^4.

A 16 B 252 C 260 D 256

Question 23

Evaluate 4^2.

A 12 B 16 C 8 D 20

Question 24

Simplify: 2^6 × 2^3

A 2^18 B 2^10 C 2^9 D 4^9

Question 25

Simplify: 2^6 ÷ 2^4

A 2^24 B 2^2 C 2^10 D 2^3

Question 26

Simplify: 3^4 ÷ 3^2

A 3^2 B 3^6 C 3^3 D 3^8

Question 27

Simplify: (5^3)^2

A 25^3 B 5^1 C 5^6 D 5^5

Question 28

Simplify: 6^5 ÷ 6^4

A 6^9 B 6^20 C 6^1 D 6^2

Question 29

Simplify: 8^6 ÷ 8^3

A 8^4 B 8^9 C 8^3 D 8^18

Question 30

Simplify: 4^5 ÷ 4^3

A 4^15 B 4^8 C 4^2 D 4^3

Question 31

Simplify: (5^4)^5

A 5^20 B 5^9 C 3125^4 D 5^-1

Question 32

Simplify: 4^6 ÷ 4^3

A 4^3 B 4^4 C 4^18 D 4^9

Question 33

Simplify: 9^5 × 9^3

A 9^9 B 81^8 C 9^8 D 9^15

Question 34

Evaluate 4^3.

A 64 B 60 C 68 D 12

Question 35

Evaluate 5^2.

A 20 B 30 C 10 D 25

Question 36

Simplify: 4^4 × 4^3

A 4^7 B 4^12 C 4^8 D 16^7

Question 37

Simplify: (2^4)^3

A 2^12 B 2^7 C 2^1 D 8^4

Question 38

Simplify: 7^5 ÷ 7^2

A 7^7 B 7^10 C 7^4 D 7^3

Question 39

Simplify: (9^6)^5

A 9^11 B 9^30 C 9^1 D 59049^6

Question 40

Simplify: 7^5 × 7^3

A 49^8 B 7^9 C 7^15 D 7^8

Question 41

Simplify: 9^3 ÷ 9^2

A 9^2 B 9^5 C 9^6 D 9^1

Question 42

Evaluate 5^4.

A 620 B 625 C 630 D 20

Question 43

Simplify: 2^2 ÷ 2^2

A 2^4 B 2^1 C 2^0 D 2^0__0

Question 44

Evaluate 3^4.

A 12 B 84 C 81 D 78

Question 45

Evaluate 2^3.

A 8__0 B 6 C 8 D 10

Question 46

Simplify: 2^4 × 2^5

A 2^9 B 2^10 C 4^9 D 2^20

Question 47

Simplify: 9^5 × 9^5

A 9^25 B 9^11 C 9^10 D 81^10

Question 48

Simplify: (5^3)^4

A 5^7 B 625^3 C 5^-1 D 5^12

Question 49

Simplify: 9^4 ÷ 9^3

A 9^12 B 9^1 C 9^2 D 9^7

Question 50

Simplify: 2^3 × 2^2

A 2^5 B 2^5__0 C 2^6 D 4^5

Question 51

Simplify: (9^6)^6

A 531441^6 B 9^0 C 9^36 D 9^12

Question 52

Evaluate 2^4.

A 18 B 16 C 14 D 8

Question 53

Evaluate 3^3.

A 9 B 27 C 24 D 30

Question 54

Simplify: 5^4 × 5^2

A 5^8 B 5^7 C 5^6 D 25^6

Question 55

Simplify: 3^2 × 3^4

A 3^6 B 3^8 C 3^7 D 9^6

Question 56

Simplify: (8^3)^4

A 8^-1 B 8^7 C 4096^3 D 8^12

Question 57

Simplify: 7^5 × 7^2

A 7^10 B 49^7 C 7^8 D 7^7

Question 58

Simplify: (5^5)^2

A 5^3 B 25^5 C 5^7 D 5^10

Question 59

Simplify: (3^2)^2

A 3^4__0 B 3^0 C 3^4 D 9^2

Question 60

Simplify: 8^6 ÷ 8^5

A 8^1 B 8^11 C 8^30 D 8^2

Question 61

Simplify: (9^3)^6

A 531441^3 B 9^-3 C 9^18 D 9^9

Question 62

Simplify: 4^6 ÷ 4^2

A 4^12 B 4^4 C 4^8 D 4^5

Question 63

Simplify: (4^4)^3

A 4^12 B 4^7 C 64^4 D 4^1

Question 64

Simplify: (4^4)^2

A 4^8 B 16^4 C 4^2 D 4^6

Question 65

Simplify: (3^2)^3

A 3^6 B 3^-1 C 27^2 D 3^5

Question 66

Simplify: (8^2)^5

A 8^7 B 8^10 C 32768^2 D 8^-3

Question 67

Simplify: 7^3 × 7^3

A 7^9 B 49^6 C 7^7 D 7^6

Question 68

Simplify: 6^2 × 6^5

A 6^7 B 36^7 C 6^10 D 6^8

Question 69

Simplify: 4^4 × 4^6

A 4^10 B 4^11 C 16^10 D 4^24

Question 70

Simplify: 5^4 ÷ 5^2

A 5^3 B 5^2 C 5^8 D 5^6

Question 71

Simplify: (6^4)^5

A 6^9 B 6^20 C 6^-1 D 7776^4

Question 72

Simplify: 6^4 × 6^4

A 36^8 B 6^16 C 6^8 D 6^9

Question 73

Simplify: (8^4)^2

A 8^6 B 64^4 C 8^2 D 8^8

Question 74

Simplify: 7^2 × 7^2

A 49^4 B 7^5 C 7^4 D 7^4__0

Question 75

Evaluate 3^2.

A 12 B 6 C 9 D 9__0

Question 76

Simplify: 4^2 × 4^4

A 4^6 B 4^8 C 16^6 D 4^7

Question 77

Simplify: (8^5)^4

A 8^1 B 8^9 C 8^20 D 4096^5

Question 78

Simplify: (4^6)^5

A 4^30 B 4^1 C 4^11 D 1024^6

Question 79

Simplify: 5^5 × 5^4

A 5^9 B 5^10 C 5^20 D 25^9

Question 80

Simplify: 9^3 × 9^6

A 9^9 B 9^10 C 9^18 D 81^9

Question 81

Simplify: 4^5 × 4^5

A 4^11 B 16^10 C 4^25 D 4^10

Question 82

Simplify: 7^5 × 7^4

A 7^20 B 7^10 C 49^9 D 7^9

Question 83

Simplify: (9^3)^2

A 81^3 B 9^1 C 9^6 D 9^5

Question 84

Simplify: 8^6 ÷ 8^4

A 8^2 B 8^3 C 8^10 D 8^24

Question 85

Simplify: 9^5 ÷ 9^5

A 9^25 B 9^10 C 9^1 D 9^0

Question 86

Simplify: 2^4 ÷ 2^2

A 2^3 B 2^2 C 2^8 D 2^6

Question 87

Simplify: 7^4 × 7^4

A 7^9 B 7^16 C 7^8 D 49^8

Question 88

Simplify: 2^6 × 2^5

A 2^30 B 2^11 C 4^11 D 2^12

Question 89

Simplify: 7^4 × 7^5

A 7^10 B 49^9 C 7^20 D 7^9

Question 90

Simplify: 3^6 × 3^5

A 3^11 B 3^30 C 3^12 D 9^11

Question 91

Simplify: 3^2 × 3^2

A 3^4 B 3^5 C 3^4__0 D 9^4

Question 92

Simplify: (4^3)^3

A 64^3 B 4^9 C 4^6 D 4^0

Question 93

Simplify: (2^5)^6

A 2^30 B 64^5 C 2^11 D 2^-1

Question 94

Simplify: (7^4)^6

A 7^-2 B 117649^4 C 7^10 D 7^24

Question 95

Simplify: (7^5)^6

A 7^-1 B 7^11 C 7^30 D 117649^5

Question 96

Simplify: 6^4 × 6^3

A 6^12 B 36^7 C 6^8 D 6^7

Question 97

Simplify: 3^5 × 3^3

A 9^8 B 3^9 C 3^8 D 3^15

Question 98

Simplify: 9^2 × 9^3

A 9^6 B 9^5__0 C 9^5 D 81^5

Question 99

Simplify: (3^2)^6

A 3^-4 B 729^2 C 3^8 D 3^12

Question 100

Simplify: 2^6 × 2^6

A 2^36 B 2^12 C 4^12 D 2^13

Ready to build steady progress before the next NAPLAN check-in?