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Indices - basic rules 2023

Total questions: 39

Worksheet time: 16mins

Name
Class
Date
1.

Simplify a7 x a10

a)

a17

b)

a70

c)

a3

d)

a-3

2.
(3x2y3)2
a)
9x4y6
b)
3x4y5
c)
6x4y6
d)
9xy
3.
Write 2 x 2 x 2 x 2 in index form
a)
23
b)
25
c)
16
d)
24
4.

a × a × a

a)
3a
b)
3a3
c)
a3
d)
3a2
5.

a × a × a × a

a)
4a
b)
a4
c)
4a4
d)
2a2
6.

Write 12 × 12 × 12 × 12 × 12 × 12 × 12 in index form

a)
126
b)
127
c)
128
d)
125
7.

Find the value of

181^8  

a)

81

b)

18

c)

8

d)

1

8.
Express b2 in expanded form
a)
b+b
b)
b+b+b
c)
b×b
d)
2×b
9.

Which is equivalent to 5 × 5 × 5 × 5

a)
53
b)
54
c)
45
d)
55
10.

what is the base number in 64?

(a)  

11.

Which is the expanded form of 33?

a)

3 + 3 + 3

b)

3 × 3 × 3

c)

3 × 3

d)

3 + 3 + 3 + 3

12.
Write 5 in long form
a)
125
b)

5 × 5 × 5 

c)
53
13.

Evaluate 43 (you need to find the actual answer, not the expanded form)

a)
64
b)
4 x 4 x 4 
c)
12
d)
8
14.

a10a2\frac{a^{10}}{a^2}

a)
a8
b)
a5
c)
a12
d)
a102
15.

9593\frac{9^5}{9^3}

a)

92

b)

98

c)

915

d)

910

16.
What is the value of (-2)3?
a)
-8
b)
-6
c)
6
d)
8
17.

Which number is the INDEX? 42 = 16

(a)  

18.

5a × 3a

a)
15a2
b)
30a
c)
15a
d)
a30
19.

Write without brackets

(2xy2)2

a)

2x2y4

b)

2xy4

c)

4x2y4

d)

2(2xy2)

20.

Simplify:

25x65x3\frac{25x^6}{5x^3}  

a)

20x3

b)

5x9

c)

5x3

21.

Simplify the following 3× 2× 3× 28

a)

3× 212

b)

312  × 28 

c)

3× 213

d)

2× 3 12

22.

12x53x2\frac{12x^5}{3x^2}

a)
x4
b)
4x3
c)
3x3
d)
4x2
23.
(3x2y3)2
a)
9x4y6
b)
3x4y5
c)
6x4y6
d)
9xy
24.

Write 6× 6as a single power

a)
7776
b)
66
c)
65
d)
365
25.

a7 × a4 ÷ a5

a)
a7
b)
a6
c)
a4
d)
a11
26.
Simplify 47  ÷ 43
a)
410
b)
4
c)
421
d)
44
27.

Simplify (x3)2

a)

x6

b)

x5

c)

x1

d)

x9

28.

Simplify (-2a)3

a)

8a3

b)

-8a3

c)

6a3

d)

-6a3

29.

Simplify

x4x2\frac{x^4}{x^2}  

a)

x1

b)

x2

c)

x3

d)

x4

30.

Simplify 56 × 54

a)

52

b)

524

c)

510

d)

564

31.

Simplify (24)5

a)

21

b)

29

c)

220

32.

Simplify

12a5b43a2b3\frac{12a^5b^4}{3a^2b^3}  

a)

36a7b7

b)

4a3b1

c)

4ab

d)

14a2b2\frac{1}{4}a^2b^2  

33.

s is equivalent to which of the following

a)

s0

b)

s1

c)

s2

d)

1

34.

Simplify

4a3b4 × 3a2b6

a)

12ab

b)

12a10b5

c)

12a5b10

d)

1

35.

Simplify

(a2)5a2a7\frac{\left(a^2\right)^5}{a^2a^7}  

a)

1

b)

a0

c)

a or a1

36.

Simplify

x17(x3)5\frac{x^{17}}{\left(x^3\right)^5}  

a)

x17

b)

x15

c)

x2

d)

32x

37.

Simplify

6x4y33x2y\frac{6x^4y^3}{3x^2y}  

a)

2x2y2

b)

2xy

c)

2x6y4

d)

18x2y2

38.

Simplify

(p3)5

a)

p2

b)

p15

c)

2p

d)

15p

39.

Simplify

n4 × n3 × n2 × n

a)

n

b)

n24

c)

n10

d)

n0